Not sure what could be the problem. Maybe the disc got corrupted somehow (unlikely) or your AV software is interfering with the installation (more likely). Even if it seems improbable, the scratches still could be root of the problem. So, what could you do? Well, I see three options:
1. Send a mail to support. They should be more able to handle your problem. Even if not, they can probably give you better advice than I am.
2. If you registered the game with Stardock, you should be able to download it with Impulse. Impulse is now owned by Gamestop, so I don't know, if you want to deal with them. There is also the slight possibility that Gamestop doesn't have the necessary information, which could lead to even more hassle.
3. Buy the Ultimate Edition. This is probably the most hassle-free option. You can download it directly from Stardock, don't require any discs for installation and the game is already fully updated. Even with the Gold Edition you would still need to use Impulse to get the patches.
I hope, that was helpful for you.
