Wishbone: Have you tried doing a traceroute to GOG.com?
MrLongPants: Sorry for my ignorance but I don't know what that is
No need to apologize, it's not something most normal users ever do. I'm going to assume you're on Windows. If not, someone else will have to help you.
Here's what you do:
1. Open a command prompt. You can do this by holding down the Windows key and pressing "r". In the window that opens, type "cmd" and click Ok.
2. In the command prompt window, type "tracert www.gog.com" and press enter. It will think for a while, and show you the list of servers it passes through on its way from your computer to GOG's webserver.
3. Copy that list (you will need to right-click in the command prompt window and click "Mark", then mark the whole thing with your mouse, and finally press enter to copy it to the clipboard). Then paste the list here, but remove the first 3-4 entries so people can't identify your machine specifically (this is just a precaution against ill-intentioned individuals and bots, the same reason you should never post your email address on a public forum).
As an example, here is my route to GOG:
5 7 ms 8 ms 8 ms ae1-0.alb2nqp7.dk.ip.tdc.net [83.88.21.83]
6 9 ms 11 ms 9 ms ae12.bar1.Copenhagen1.level3.net [4.68.71.9]
7 43 ms 43 ms 45 ms ae-1-17.bar2.Warsaw1.Level3.net [4.69.153.74]
8 48 ms 44 ms 44 ms ae-1-17.bar2.Warsaw1.Level3.net [4.69.153.74]
9 77 ms 44 ms 43 ms 213.242.109.58
10 42 ms 40 ms 41 ms rev-46.229.152.117.atman.pl [46.229.152.117]
11 41 ms 40 ms 41 ms host-2129120-107.gog.com [212.91.20.107]
What you're looking for when trying to determine routing problems are entries with much larger ping times than the others (indicated in ms, miliseconds).