I'm a first time poster as I've never had any problems with my 1995 Monte Carlo LS. I've also not posted because it's stock with a 3.1 V6 and OD automatic transmission.

Some history on the car:
I changed the batter in September 2005.
I replaced the starter with a Duralast gold approximately 2 months ago.
Twice since replacing the starter and solenoid as a unit, I've had to short across the solenoid to get the engine to turn over. I noticed the plastic part of the solenoid where I connected the cables is now loose. I've not taken the starter back out to fix it yet.

My problems
Two days ago, with no warning, the battery was dead.
I got a free replacement and, when I connected the battery terminals, I noticed the back up lights were on. I've shifted the car into every gear and the lights won't go out.
Next I tried turning the key to get the lights out, but no luck.
When I turned the ignition off, the car kept running! I had to pull a fuse to kill it. Of course the lights stayed on. I tried re-starting and turning off the car and the same thing happened again, resulting in the fuse being pulled.
Another unrelated problem is that neither of the electric fans spin when the engine is idling. They work fine when the car is in gear, but I've had the temperature gauge almost redline with the engine idling and the fans unresponsive.

Does anyone know what is going on here? Help would be greatly appreciated as this is my only car. Thanks for any help.

 

Update: I changed the starter and solenoid again, so that problem should be solved.

The back up lights are still on with the battery connected and the car still won't tun off. Everything in the column appears to be functioning properly.

EDIT: I forgot to mention this before. The car is column shifted. I don't know if all 95s were, but my cousin who owns a 96 was under the impression it had a floor shifter because his does.