2002 Ford Escort

We bought this Escort a few months ago for our daughter. It ran great. It started out cutting off some when she was driving down the road the radio would also go off. She would coast off the road, put it into park or neutral and it would start right up. It may die again shortly or may run fine for several weeks. It has now a couple of times not started a couple of times. When it does not start it is completely dead, no interior lights, no exterior lights, nothing. The battery connections are tight and the fuses in the fuse box appear to be intact. One time I shifted it into neutral from park and it then started right up. Another time I just opeaned the hood and it started right up. When it did start the clock had reset to 12:00 and all the radio presets were lost, like the battery had been disconnected. It has a new battery, new plugs and wires, new ignition coil and throttle body (I think that was it) was cleaned. Please help!