Since the engine you bought was probably sitting, I would pull and clean the oil pressure switch to verify that it isn't clogged. If the switch senses a drop in oil pressure (plugged up screen) it will kill the engine to prevent damage.
You might also not have a "run" circuit going on the fuel pump, and be running off the primer. It will push enough fuel to run for a few seconds and then stall. Keep reading the fuel pressure gauge while it stalls out, if it has a check valve (a lot of them do) make sure it is held to bleed down with the system.
The other most likely possibilities would leave you with codes, and since you have none I won't go through them. Just double check and verify you have everything plugged in, that would alleviate most of the potential issues.
The computer should not matter, I switched my computer out just to test the system on my car. Even after doing so, i did not need to do a relearn to get it running. In fact, I had never done a relearn on my aveo while I had it, and I pulled all kinds of things on and off on a regular basis.