Thanks for the post. You're probably right about the MSSQLSERVER part. Meaning the server name that I need to specify is either ANGEL-G71G or (local). Both work so I guess I'll use one of them.
I was really pissed of because I created the "NT AUTHORITY\IUSR" and gave him ownership rights, but it still didn't work for some reason. So I enabled all connection types, specifically named pipes and tcp/ip. It still didn't work. Enabled the SQL Server Browser and User Agent, and it still didn't work. Turned off all SQL Server services, and started them again, and it still didn't work.
Added the connection string Server: ANGEL-G71G into IIS. This could have been it, I have no idea.
Then I removed all previously created custom users for SQL Server, restarted the lappy, created the 'NT AUTHORITY\IUSR' and it worked.
I know this may not be the safest way, but I just need it to work for a presentation. For the security and actual realization of the project, I'll read more about SQL Server when I'll be doing that.