The battery could be shorting out. These cars do really funky things whent he batterys are dying. And yes, the car can and does start OK in some of the se cases. You could have a bad alternator. You could also have a bad or dirty battery cable. If the battery checks out ok you should check the ground bolt that is under the battery tray. I've seen them get corroded and cause sparatic electrical problems. Worse case is a bad wiring harness. It is a 95 and I've had several with bad harnesses.
