This might not be the reason, but I've noticed that some older DVD-ROM (or DVD-RAM, acutally) drives have trouble reading certain types of DVD-R or -RW media. I had the same problem with early CD-Rs; the blue Verbatim ones wouldn't read in a lot of older CD drives.
It could also just be dirty and/or failing--it's pretty old, after all.
You might try a different brand of discs, or maybe just replace the old DVD-ROM drive with a newer one--heck, you can get a brand new DVD-/+RW drive for like $35 now.