Mitsubishi Repair: 1990 Mitsubishi Eclipse, mitsubishi eclipse, fuse box

Question
I've got an eclipse I'm trying to trouble shoot and figure out. First thing the car has a different motor its a 1990 Mitsubishi eclipse with a 2.0 16 valve turbo motor and is a 5 speed manual. The car had a dead battery so i hooked up a new battery and the car is in neutral and will not turn or start all you hear is a click sound behind dash the windows dont go up or down the cd player dont come on the wipers are really slow when they come on the dome lights are stuck on with the doors shut the clock on cd player stays on and the open door idiot light stays on. So my guess from past experience would be the key ignition switch the switch the key goes into and turns all the lights n starts the car with is bad cause i had a ford escort switch go and it caused the stuff to stay on. So my question is what else or does it def sound like the key switch is bad. Please help the car was running fine then all of a sudden ran rough it was fixed by cleaning the plugs then it ran find and smooth then just wouldn't start one day I'm  told the engine is not blown the car was taken care of just wondering why it wont start or not everything's working. Other thoughts i have in mind could be alternator and the starter but the issue with the domes and door open lights on to me sounds like the key switch or maybe even that and the ignition switch or something im not sure please help.

Answer
Rick,
The electrical problem can caused anywhere in the circuit between the fuse box to the steering column switches; ignition switch and light control switch.  If an aftermarket radio was installed, there may be an electrical problem somewhere there.  For the issue where the dome light is staying on, you should check the door switch, located on the lower part of the door sill.  I had a problem where the dome light would never turn on, but my problem was due to the door sill contacts being overly corroded.  You may have a similar problem.
Good luck!