I'd check the fuel pump relay/fuel pump.

 

I had the problem, changed my fuel pump to a higher flow and it didnt change it. Turned out being the distributer was advanced to much, when you turn it with the ignition on engine off you can hear certain injectors fire.

 

I had a problem very similar to what you are describing, engine would start up and then die, start right back up and then die. It turned out my mass air flow sensor was bad.

 

put a code scanner on it see what it brings up, and if nothing there
check fuel pump relay(under driver seat) borrow one to try it before you buy one, like the post above it could be your mass air too

 

he's got an 88, no maf...

 

i had an 85 i did a bunch of work to that did the same thing......got it to run and took it out the driveway like you said and it died......turned out the ignition switch was bad.......

 

ignition switch all the way man. Try slowly pulling the key back after moving it to the start position. if it stays on longer, you know its the ignition. Mine is VERY touchy, but I have been able to learn how to start it without it doing anything funny.

 

mine is an 88 gt and it does have a mass air flow sensor i think it was a california car but hey guess what guys i dont kwno what the hell happened but today i was when and turned it on to start messing with it cause i had been at work and gues what happened it started and stayed on didnt turn off and i turned it off and started right back up and now it runs fine i guess it has a mind of its own and didnt feel like going for a ride lol but thanx guys for all your info and help again you guess really help use alot

 

check your fuel pump, all vaccuum lines, fuel filter and all of your intake. also if it is cold in your area, throw a can of gas line antifreeze in your tank or a can of drygas, your fuel rails could be frozen. it also could be an O2 sensor, although that probably wouldnt do it as consistantly as it sounds like youre having this problem. good luck, let me know how you make out