are these DVD's commercially produced or ones that you have made yourself?
If home-made ones, do commercial ones mount on the desktop?
Try restarting and repairing permissions, although that does not do a lot in 10.4, but it's worth a try.
I was attempting to back up a few of my DVDs and place them into iTunes; however none of the DVDs I've tried have mounted to Finder. Handbrake recognizes that there is a disc but at the end of encoding it locks up. When I first insert the DVDs, the DVD Player opens to a blank screen and if I try to go to a menu or play it says no supported disc. I've played DVDs successfully before so this problem is less than a week old.
Intel Core 2 Duo
Mac OS X 10.4.10
8x slot-loading SuperDrive