I think I've figured out what the problem is though. My dad recently purchased a Sony CFD-S20CP, a boombox type radio/CD/tape player, but it has the ablility to play MP3 CD's. He wanted this player so that he could set it up to have multiple CD's worth of music to play.
I have helped him along the way, from getting CDex set up so he can rip his CD's to MP3's using LAME (which is built into CDex) to burning them to CD. If i burn a disc in my drive (CD-R or CD-RW, it doesn't matter) the disc reads and plays perfectly in his player. If I do the same thing in his burner, all hell breaks loose. After reviewing all the settings in Nero, my guess is that the problem comes down to the fact that I have my drive set to burn Disc-At-Once, while his drive is set to burn Track-At-Once. Hopefully this is the root of the problem, and we will be able to correct his settings in the morning. If not, I guess we'll just have to burn all the MP3 discs on my computer.
We'll see what happens...
Update: The burner was not at fault. The installation of CDex was corrupt. After reinstalling on his computer, everything is peachy.