The motor running may be the central locking vacuum pump, I believe that on a coupe it's under the right side of the rear seat, inside the car. It would make sense given your description. Is the central locking system working OK? Should be locking the gas door and the trunk, make sure they work, and of course both doors. If one isn't working, the motor will try for awhile, then quit trying, this may be what's going on. I doubt it is the cause for the battery to go dead.
This could be many things. Try the trunk light, push down on the probe (with your finger) that is pushed in by closing the trunk and see if the light is actually going out. Make sure there is nothing electrical still on. Are you familiar with the light switch? It must be pointing up to the 12 o'clock position, if you turn it to one of the clicks to the left of "O" (12 o'clock) there is a side marker option that will come on when the key is off, I've had a few roadside calls for this happening. There is a switch on the dash for the rear domelight, make sure that is off. Might be a good idea just to go walk around the car in a dark area, in the garage maybe. Maybe something will be obvious then.
Other than that, I'd say the resting current draw will need to be checked, while pulling fuses one at a time to isolate the problem and go from there.
Oh, are you sure the battery and alternator are good?