Sounds like a fun project! Assuimg the new engine is mechanically and electrically sound, it’s probably something simple, but what it is may take some time to find. Why the reference to the automatic transmission? Do you mean you not only installed a replacement engine, but a replacement automatic automatic transmission too? Please clarify the engine and xmission config of both cars prior to and after the swap.
And engine should crank for more than 3 seconds, whether it runs or not. Maybe start with that, as it should be easy to diagnose, and may point you in the direction of why it doesn’t catch and run. Have you had the battery load tested? Have you measured the voltages at both starter terminals during attempted cranking? Edit: Measure between the terminal and the starter case.
Other than that, if you are certain the fuel pressure is ok, and it is injecting fuel from the fuel injectors, and you have a good visible spark at the spark plugs, then the problem is likely among
- Ignition timing
- Valve timing
- Fuel/air mixture
Those problems are best addressed using the diagnostic software provided on the car’s ECM. Are you able to read the DTC codes?