1995 Chevy S-10 Starting problem

I replaced the alternator in my truck and a couple days later, it wont start. The starter tries to turn over, the batter is good, and that alternator seemed to be working fine. The last time I drove the vehicle, it died a few times after starting it and after a while started and I drove it home. It hasn't started since, and when I turn the key on everything works except the dash lights. They fade on and flicker then go out when I try to start the vehicle. Before the alternator was replaced, the spedometer would sometimes stop working when the heater was turned on but the vehicle didn't run long enough to see if that has stopped. What would cause this problem?