'84 Firebird issue, please help

Hey guys. We just got a 83 firebird, and we love it, and the test drive went fine. But after getting it home, it wouldnt start. We replaced the fuel pump relay, fuel filter and the fuel pump itself. It ran finally but sputtered off and we couldnt get it going again. A mechanic friend of mine says could be the ECM, the computer. Anyone have any other advice? Thanks. We are very frustrated.

Can you get a new ECM? They look to be between 30 bucks and maybe 80 bucks, used, online. Replace it and try it out. It could also be the distributer. It could be overheating. Try letting it sit overnight and see if it runs OK the next morning. I would spring for the ECM and see where you are after that.
https://www.youtube.com/watch?v=e4t5OXpDcig