I opened up my Alienware to clean it out and when I put it back it wouldn't light that side up any more. Not quite sure how that works, but I'm pretty sure I put it back properly and completely so it should light up.
I don't know how these light up or anything but you could check and see if there is a ground disconnected or maybe you jarred the bulb and it broke, maybe static blew it. Tried googling this? Sorry I can't be of more help than that.
On the left side (inside of the door) there is a small connector that looks like it has 6 little copper pins on it. It is located near the rear of the door. Check to make sure that the pins are making connection to the plate in the same location (side of the PSU) in the lower rear of the system. The connector that allows power and signal to change colors in the door panel is a touch type connection. Meaning there are two parts, and as they push together, they keep connection. Check to make sure that the plates on the PSU side are clean. Also check that the small pins on the door side are sticking out a tiny bit. It is possible that the door is not sitting in its groove at the back, it could still latch but not be in the groove. Try removing the door, then setting it in, bottom first into the little notches cut in the bottom chassis rail, and then pulling the door in tight at the top. If that has no effect, try powering the system off, unplug it for a short time (at least 5 minutes), then plug it back in and restart, and see if it is working then. If it is not, then the only other option would be to call Alienware Tech and see if they have any advice, and if they can send out a tech is you are in warranty.
But for basic description, the connector that sends power for light and the color signals to the LED lights is near the rear. This connector also triggers the service lights inside the chassis to come on once the door is opened. So check to see if those lights have gone off (look thru some of the vent holes at the back). If that service light remains on with the door closed, then the pressure connections are not making ANY connection at all.