When I try to boot the game, it doesn't register anything in the DVD Drive, and I'm unable to dump it using 13xforever's disc dumper. Any help would be appreciated.
It's not a DVD drive, it's a Blu-Ray drive.
See if it shows contents when you browse into the disc when you put disc in. If it does, then the drive is working fine. Otherwise you may have some revision and/or firmware version that doesn't support PS3 games.