1. The "FAT" model PS3's are known for their bluray drives going bad. Many argue that it is caused by firmware upgrades, but we may never know what truly causes it.
Have you tried any other disks besides games?? Try a bluray movie, regular DVD, and also an audio CD. There are two separate lasers in the drive. One for Games and Bluray DVDs, and another one for DVDs, CD, and PS2 games. If it plays DVDs and CDs but doesn't recognize Bluray DVDs or games, then the bluray laser has most likely failed.
It is a fairly easy to change the drive out or just the just the bluray laser. Plus, it's not terribly expensive if you're willing to give it a shot!
If you'd like to attempt the repair use the ifixit guide below:
PlayStation 3 BluRay Laser Replacement
2. As for the games downloaded directly to your console:
You CAN and WILL be able to play downloaded games. This is ONLY way you will be able to play games on your PS3 in the future until you replace the bluray drive.
Hope this helps!