When you pulled the dome light was there 2 wires or 3?
If there are two wires one should be wired to the door switch (pos) and the other wire should be ground. If this is the case the only way to change this would be a lot of work. Easiest route would be to run a new power wire. Either independent of ignition with a ignition relay depending on if you want it to run with the power on or off.
If there are three wires. one should be wired to the door switch (pos), one to the ground, and the third should be wired to the ignition power. The ignition power is the one you will want to use. for the DVD player.
Basically without running any new wires you can only do what the dome light could do. If it only turned on due to the doors this is it without messing with circuit boards and relays. If you could flip the switch which I don't know much about first gens and have it stay on then that is the wire for the DVD player you should use. Now will the default wire be able to supply enough power that is a whole different story that someone much more knowledgeable then me will have to tell you.
