Well I finally got my 85 Z started and it seems I don't really know why. The timing was correct and fuel and sparkwere not tampered with before hand leaving me no reason to why it didn't start before. Now after I got it started I adjusted the amount of fuel in the carb sight glass and touched up the idle and fuel flow to get a good smooth running engine. I then drove it for a while and all was well. No more backfiring and no more sputtering when I was driving. All seemed well.
Then this morning I got up(excidedly because I was going to be able to drive the car) and it turned over like everything was ok and then it was all downhill from there. It started on the second turn of the key and was idling awefully. It was shaking and wabling at around 500 rpm and then it died and it wouldnt start again after that. I have no idea what could have happened between yesterday afternoon and this morning. PLEASE HELP!!! This is driving me crazy. I don't know what else to check.

does it have an electric choke? if so, is it hooked up and adjusted correctly?
did you gicve it a couple of pumpes before cranking it to set the choke and get the carb on fast idle?
after it starts, can you keep it runing by giving it some gas? or does it die no matter what?
a little story..
one of my friends in high school had a nice 76 Cutlass with a Holley carb on it. all he knew before that was fuel injected cars. he REFUSED to pump the gas to set the choke before cranking it, and also REFUSED to pump the gas while it was cranking to help it to start. his dad (not a car guy by any stretch of the definition) told him to never hit the gas while cranking because "modern" cars can be hurt if you do that.....
it always took a while to start, if it even would fire at all.
well, it wouldn't start for him one day after school, so i tried it. one pump of the gas and it popped right off, and a couple of blips to clear it out and it smoothed right out and purred like a kitten.

Yeah, I pumped the gas a couple times before attempting to start but it did not use. I know it is getting fuel. I do have an electric choke that was set too closed, but I adjusted that yesterday, let it cool off a little and tried again to no avail. After toying with it a little yesterday I think that it may be a distributer problem. I am getting spark, but it is a weak one. Also when it was running the other day I was letting it idle for a while and the idle just dropped off for no apparent reason. A friend who is helping me says that he thinks that it might have been the distributor going bad. It makes sense seeing that I have has this sort of problem before and maybe this time it just had enough. I am going to widen the gaps a little on the plugs and see what that does first though. By the way, does anyone know the correct gap size for a 350 w/ Demon Jr 725cfm carb. Thanks for the input again.