I recently had an old DVD drive that did the same thing. It worked fine for CD's, but didn't recognize DVD's at all. I tried taking it apart and cleaning the rubber tire that spins the discs and the lens, as this has helped me to fix many non-working drives in the past, but no go. You could try cleaning the rubber tire (you usually can clean this with a qtip, with the tray open, to avoid taking it apart- cleaning lens though, you probably would need to disassemble and be VERY gentle with the lens)
You can TRY cleaning, but if it doesn't work, the drive is probably dead meat.
Good luck, good thing drives are pretty cheap nowadays!