1996 Infiniti I30 Car Not Starting

I was driving back home when my dashboard lights were coming on intermittently (ABS, Hand Brake, etc) and the engine seemed to want to stall. The head lights also dimmed and the radio stopped playing.

Somehow I made it back home (driving 10 miles) with almost no head lights and most of the dash lights on. I turned the car off and then tried to restart - nothing at all. No starter sound at all. After letting the car sit for 24 hours, I tried cranking it and the starter turned over once before it going to a full click sound from the battery. Eventually after 2-3 tries, the click sound also stops and there is no effect of turning the key.

I checked and cleaned the battery connections. Battery seems to be working well. I recently changed all 6 spark plugs (about a week ago). Started and drove the car a dozen times till this happened.

Any pointers where to begin would be helpful.