I have a 1996 Dodge Neon. No features, not even A/C or power windows.

2 days ago I was trying to drive home from work. I started the car, backed out of my parking space, shifted from reverse to 1st gear, and as I started to accelerate, the engine died, dash & head lights shut off and the radio went silent. I tried to start it and the started didn't engage, the relay didn't click... NOTHING. The only things that worked (sort of) were the accessory outlet(cigarette lighter) and the oil light. I turned off the head light switch and the key and the oil light turned off. I turned the head light switch on and the oil light came back on (without the key in the ignition). turned the lights off and opened my door to get out. Dome light didn't turn on, oil light started blinking and a relay in the interior fuse panel started clicking rapidly in time with the oil light. The next day, I came back to my car and the battery had been drained overnight while the lights, and everything were shut off. I think it might be my ECM. I am open to any help anyone might have.