Welcome to the forum.
What engine, transmission?
Why the PCM swap?
Did the engine start and then shut down in a few seconds? If so, that is a security issue. The part numbers may be the same but that doesn't mean it was programmed the same, it's a computer.
Make sure the battery cables are on tight and the tranny is in P or N. What happens when you turn the key to start? There should be a relay for the starter motor in the PDC under the hood - and you should hear it click. There is also the solenoid on the starter motor itself.