dash lights; heater, car dies

[Darjean]

I have a 1996 Cadillac Deville sedan. We are the second owners and I have the repair history; it seems that these problems have been ongoing since 48000 kilometers (every 20000 k's) and the dealership comments they "cannot duplicate customer concerns", so it seems there is a significant history of these issues. I've been having problems with the dash lights going off and on intermittently, the heater comes on and cannot be turned off. I've cleaned all the battery terminals but this hasn't helped for very long. As well, the car will start but then immediately dies. I can eventually get it going after several tries and time out. Today after 50 kms, all the dash lights went out and flickered on and out for the rest of the trip. Is it possible that it is the battery relay? Any other suggestions? Does this sound like an electrical issue?