I have been having this nagging problem with my civic since I bought the car. When I try to start the car, it will just crank and make no effort to run. I have to wait 1-10 minutes inside my car for the check engine light to blink and then the fuel pump primes. Once the car does that, it fires right up. Any time I turn it off again, it will do the same thing. This is a list of items that are new on the car:

Fuel Pump
Fuel Tank as well as good gas
Main Relay
Spark Plugs/Wires
Distributor
have 2 P06 Ecu's which do similar things on the car. Both have had the capacitors replaced.

Would anyone have an idea as to what is causing this issue? I have also checked grounds and found them to be correct. I still think that this is an ECU issue but want to be completely sure before I go out and buy a refurbished one and have the same issue.

 

I had a similar issue after my wife's 93 Civic EX original ECU fried from leaking electrolytic capacitors.
I had bought a rebuilt ECU from Advance Auto Parts and it failed within a few starts.
Their replacement ECU for the first rebuilt one, would take several minutes (I think around 3 minutes or so) before all the relay clicks were made and then it would start.

I said the hell with them and went on eBay and bought two used one's. One is in the car and is still working right while the other two (one Ebay one was slow as well)
will finally make it through all the start up relay clicks after a few minutes or so are in the trunk as emergency spares.

I think ECUs can be hit or miss and your original one before your engine swap may be your problem.

 

If the capacitors have leaked, more extensive work than just replacing capacitors will be needed to clean up the leaked liquid and repair any damage to the circuit traces or other parts from the leak.