| I, too, have had this conundrum hit me. I also found out what xunker knows, that there are PCI-based cards to drive flatpanels. The most common use the same chipsets likely found in your laptop: Cirrus Logic, Chips & Technologies, or NeoMagic.
The one useful thing I have to add is that you must be careful about your power supply. The LCD panel requires power (not much of it, natch) but in some cases may expect to draw this power over the interface (there's a separate cable for it, but sometimes it's integrated into the connector). Well, if you have a hodge-podge PC built from older stuff with lots of slots filled (as many of us might, as that's just the sort of box that would be ideal to hide under the bed and put a small panel on) you may find that your bus doesn't have the power to run the panel. If this is the case, you'll either get a machine that refuses to boot, or one that shuts down unexpectedly - a lot.
The best thing to do is wire the power circuit for the flatpanel into another power source - either over the keyboard bus or from an external power supply. Careful, though; doing this running a cable into the PC and splicing into one of your power supply drive connectors will only work iff your flatpanel happens to need the same voltage - which is unlikely. Make sure you check.
For those who want to try this, the hi tech cafe (www.hitechcafe.com) and The Computer Geeks (www.compgeeks.com) sometimes liquidate spare parts including laptop displays... | 
