My best guess would be either the battery is bad, the alternator is bad, there's a faulty wire somewhere or the positive/negative battery cables are corroded.
Also: "A battery problem can be diagnosed by looking at how the the electrics in the car behave when the no-start occurs. Turn on the headlights and either have someone watch them or just look at any bright dash light, then hit the starter. A good battery but a failing starter (or ignition relay or ignition switch) won't supply current to the starter and the car's voltage will stay high and the lights will all stay bright. A failing battery can't supply enough oomph to start the car and when you hit the starter the current drain to the starter pulls down the voltage to all the lights and they will dim, or even go off. So, bright lights while failing to start = bad starter or ignition switch, dimming lights while failing to start= bad battery or bad charging system (the battery isn't getting recharged when the car is running)."