2004 Nissan primera 1.6 petrol has cold start problem not battery not starter

So what happens when you tow a vehicle, the fuel delivery remains the same, (assuming the fuel system is set up correctly and is fully funtional.)
The spark is present ?
I would go back to basics. For a start , has it been scanned with an OBD reader to diagnose the issue?
You have changed the cps and no joy. You have changed the throttle body, is the throttle body. Are the throttle position and the pedal position sensors located on it? If not, are they functioning ?
If the vehicle only starts intermittently when being towed you must have an intermittent fault with another component.

I would1 carry out a compression check
2have the OBDsystem scanned
3Check fuel delivery, fuel pressure from the pump is typically about 40psi

check that you have spark when hot and cold, check the resistance values in the ignition system. ensure you have a good spark.
(might be an ignition issue, i.e. an electrical problem.5
Ensure that enough air is getting into the system, i.e. clean filter.

once you have established thet you have checked the trouble should be revealed, there is nothing else it can be really if all the above prove ok .....apart from a faulty ECU perhaps.

Incidentally, don't know if you have this where you live, but a TERRA CLEAN will do it a world ofgood .

GOOD LUCK