I've done some investigating and it appears that the Teacher's console in Lab B is flaky in one way or another. It's either a hardware configuration problem or a software installation problem (as in conflicting instructions on what to do when a DVD is inserted). I've tried turning off autoplay but that doesn't help.

I installed the very same KLite Codec pack in Lab C and RealPlayer happily starts to play the DVD. The teacher stations are identical in terms of hardware and software, so I will take a look at Lab B and do the following:
Merge a reg file I created from Lab C.
If that doesn't work I'll uninstall all aftermarket media players (QuickTime, RealPlayer, VLC etc) and see if the problem persists.
If it does I'll start looking at the configuration of hardware