You need to be sure that the engine is actually enabled, i.e. the orange "key" symbol on the dash goes out.
I had something similar a few years ago when I did the same swap to the same car... in my case the fuel was not getting through and I left it with a Fiat specialist with diagnostics etc. He found a bad wire on on of the ECU multiplug connectors, fixed that and everything was fine.
Assuming you got the correct (i.e. later) engine for the car, it sounds like something fundamental (and maybe simple) isn't right and you may need experienced assistance to track it down.