1996 Honda Accord Strange electrical or computer problem

After a cross country trip with no mechanical problems I parked the car and immediately noticed that the electric door locks didn't work. I tried to start the car and it wouldn't start. After waiting a few minutes I tried again and the car started but the clock had reset to 0:00. This happened again later in the day.

The next day the car started but after a few miles the ABS lite came on. When I stopped the car I experienced the same problem as before but the car wouldn't start. I noticed that the interior lights on the car worked until I turned the ignition switch then the lights would die. No click or anything with the ignition switch. Turning the ignition switch would turn off the lights.

I unhooked the battery, waited 5 minutes, then started the car and it turned on. I drove the car to the dealer for repair. For some reason the throttle was cycling fast then very slow when in park at the dealership.

The dealership can't replicate the problem but wants to charge $270 to replace the battery cables and $540 to fix the throttle. I don't think either of these repairs will fix the problems.

Any ideas?

Keith