Okay, so I got my dad's two PCs that he has at work. I need to format them. I must use Vista because their old software doesn't work with Windows 7 for some reasons (it says that it is missing some files or something, even when I use the compatibility settings, and they are used to using Vista anyway).
PC number 1:
When the "Copying Files" finishes and "Extending Files" begins / or somewhere in the middle of it, the PC just restarts. I don't freaking know what might be the problem. I tried using an older DVD ROM drive, thinking it might be the drive that makes the problems. But its not that. I still restarted a few times, but a "miracle" happened and it finished.
I really don't know what the problem is, and I've noticed that the PC was restarting on itself from time to time (before I formatted it). After it was done with the formatting, it again restarted once. So I decided to clean all the dust inside the case, remove everything, and put everything back, and I also removed the 512MB RAM (but left the other 2GB (it had 2GB + 512MB sticks)).
So far, it is working fine.
So whats the problem here? Well, that was the first PC and it was the first time that this has happened on this one. I had the same problems with the second PC several months ago (and used cloning as a workaround for the restarts during the formatting).
Both PCs are identical. In a few days, I will be formatting the second PC, and I'm sure to run in the same problems again. Any ideas why they keep restarting?

Most common reason for random reset :
- Defective Ram - Try downloading memtest86 livecd and let run for serveral hours to make sure your ram is working correctly.
- Temperature issue problem - Make sure that all the fans, I mean the CPU and GPU fan, a defective CPU fan can result in the PC reseting without any blue screen or any warning.
- Chipset driver missing - Shouldn't happen with Vista or Seven but if you use SATA HD in AHCI sometime the default driver bundled with Windows doesn't work correctly with your chipset, in this case download the correct driver and tell windows to use it during install.

Thank you for the reply. I will test the RAM during the weekend (thats when I'll be formatting the second PC). On another note, two hours running, the first PC hasn't restarted. Who knows, it might have been something with the cables or the RAM stick I removed. But will also test this one together with the removed stick during the weekend.
About the fans, I checked all of them on the first PC, I didn't notice any problems, they were all working fine during the time the case was opened (few hours). Will check the fans on the second PC before formatting.
EDIT: I'll install all drivers, of course.

Unexplained restarting could be caused by any of several things. If it still happens after updating the chipset drivers, a hardware issue is a possibility.
First and foremost, undo any overclocks you may have applied and reset the BIOS. You can try loading the default settings (whatever it calls them). If you can't find the setting or it doesn't help, turn the system off completely (also turn off the power supply, if it has a dedicated switch, and unplug the power cord) and remove the battery for a minute or so before replacing it and starting the system again; the exact time needed for this to work varies widely, but you'll know when it has worked because the BIOS clock will reset to a time in the past and you will most likely get a warning message about the BIOS loading defaults or some such thing.
If you still get unexplained restarts after that, the next easiest thing to try is a memory test. Grab a copy of Memtest86+ and burn it to a disc with ImgBurn (both are freeware). Restart the computer and boot from it. It will take a very long time to run but will eventually identify faulty RAM if that is the problem. If it identifies a fault and your RAM is on multiple modules, remove all but one and try again, repeating (always in the same slot, ideally starting with slot 0) until you find which one is faulty; if the 512MB is on a single module, try swapping it with some other RAM to see if that eliminates the problem. If it identifies all the RAM you try as being faulty (which is possible but not very likely) repeat the process with the next slot.
If a memory test doesn't indicate a fault, or putting "faulty" RAM in a different slot makes it show up as valid RAM, the motherboard may be to blame, but that's another story. Anyway, see how you get on after a BIOS reset and memory test.

BIOS reset is out of the question. I did that when I was having the same problems formatting the second PC several months ago. It did not help one bit.
I have not made any overclockings whatsoever. Also, I always check the BIOS settings before formatting. I didn't notice anything wrong.
My dad needs the first PC done for tomorrow, right now I'm installing all the heavy Autodesk, Bentley, Corel and Microsoft software packages. So I can't really do a memory test right now. It might have been that 512MB ram that was causing the restarts on this first PC. It has not restarted itself in quite a bit of time, ever since I removed that stick.
But nevertheless, I will do a detailed memory test during the weekend.
Thank you for the reply. :)
Also, I would like to excuse myself for my English and sometimes not connected sentences and stuff. I know what I want to say, just don't know how to exactly say it sometimes. Gotta work on that one.

Some good advice so far. I'd also make sure that your hardware is being properly recognised in BIOS. If not then flashing it could seriously improve stability (or could brick it entirely if you're not careful. So make sure you know what you're doing first).

First PC is done. I had one restart while booting (after I formatted it). But no problems so far.
Second PC:
The memory is not a problem. :/
I also updated the firmware of the DVD drives, but still it doesn't help. So, what now I am going to do is take out all cables, and put new cables in (not new actually, old ones that I have from an older PC).
One thing is very noticeable, there are very, very long breaks during Vista's installation menu. It takes few minutes for the Install Now screen to appear, few minutes for it to pass, and a few more minutes for you to get to the screen where you set up the partitions.
So, its either something with the HDD or the cables. I can't think of anything else.

Did you format the HDD with the Vista DVD or per command line with the default allocation size (4096 bytes <- NTFS)? One of my HDD was once formated with 512 bytes and it took the setup almost a day!! to install windows. Read and write speed was noticeably slow. It was weird.

Its like this...
I insert the disc... Change BIOS settings to boot from it. The text shows that I have to press any key to boot from disc. I do that...
It shows "Windows is loading setup files" or something like that... When that passes, the Vista background appears, and it just hangs there for like 3-5 minutes before the language screen appears. Its same for the other screens.

During these 5 mins is the drive having much activity? Like the disc slowing down, accelerating, the LED blinking fast and making noises?
Is your drive IDE or SATA? Maybe there are some features that need to be enabled in the BIOS to take full advantage of your drive, if you have your mainboard documentation at hand maybe there some more informations in there.

I've just opened the second PC...
Noticed that all the cables were connected to the second ports. So I switched them to the primary ports, but the thing still restarted during installation.
Also, I noticed that the HDD does not have a possibility for an IDE cable connection, its connected via SATA cable to the motherboard, but the BIOS recognizes that as an IDE connection. Any possible problems here?
On another note, I'll try an older DVD drive, the one that I used to install the OS on the first PC.
Its like turned off for few minutes, turning on for a sec and the screen shows up, when you click something it again turns off... The same thing again and again, for every screen during installation. The drive is IDE. Will try to check the BIOS. Sadly, I don't have any manuals for these PCs, as these were bought by my dad without me interfering in the purchase (like getting proper parts in the first place). The PCs were bought in 2007 as a whole, without retail boxes, installation discs or stuff like that.

That doesn't sound too good. I have an old PC from 2002-2003 or something that functioned with an IDE HDD but already offered SATA connections. So not too long ago the drive would die and I installed a brand new SATA HDD. To make it work I had to explicitely disable the IDE feature for Hard Drives and Enable SATA support to avoid interferences. That option was not too easy to find though, so oyu might have a look around to see if there's such option. Don't disable your IDE disc drive by error ;)
If you have look into the belly of your computer, maybe there's the name of the vendor and identification number on the mainboard. With a bit luck we might find it on the net.

I tried using a SATA drive, it tells me something ATAPI is not compatible.
I tried using older cables, for some fucking reason the PC does not start at all with them.
I tried using an older IDE drive, same thing again, the PC does not start.
Now I am using another PSU. I doubt this will work, but its better than the one that was in the case...
Will report back.
EDIT: Screens appear faster now. I cannot fucking believe this. The PSU has been fucking with me on both of the PCs in the same time? Will report in a dozen minutes...
EDIT2: For fuck's sake! Its not the PSU, the damn thing restarted again... God, I'm this close to throwing it through the window.
Reporting back...
So, either it is the whole motherboard, or it is just the HDD that is being detected as IDE, but actually is connected with the motherboard via an ATA cable. Meaning probably is not compatible with the motherboard or something.
Fuck formatting, fuck working this out. Fuck everything. I am going to try and clone the HDD, it was really the only way to do it last time I formatted the PCs.

Guess what? After cloning, it is giving me blue screen errors on start up. Its probably because I cloned it from a PC with different hardware, but basically the same software needed for work. Vista is attempting to repair the errors right now, and what do you know... it restarted as I was writing this. Ffs already with this crap.
Tomorrow I'll do another clone, from the first PC that has the same hardware, it worked last time, will see how it goes this time.