I just bought Doom 3 BFG edition, when i go to install the game it stops at 10% and says installation failed disk access error. So, I made sure GOG has full access and that my anti virus doesn't stop it but it still wont work. This issue has happened in the past when I installed other games but running GOG in administrator mode worked fine for the other games but not for doom 3. I also tried reinstalling GOG but still it fails to download, any help would be appreciated.

So, you've tried downloading and installing via Galaxy. have you tried the same with the offline backup installers?

What is the destination you selected for the downloaded Doom game? If you opted for the (original) default location it will be in Program Files (which was okay several versions of Windoze ago but is now deprecated) and that now can cause critical problems.

As @Braggadar noted, and I always do, I recommend manually downloading the self-expanding installation file and executing it (double-click in Windows in the file list of the host folder) and follow the bouncing ball to install Doom in a useful place, like
D:\Games\GOG\Carmax\Dooms\Doom 3 BFG
or whatever boosts your bonus.