Newbie help: wrong ECU in my car?

[iaint]

Hi guys. I'm new to to the forum and this is a long story so please go easy.

Bought a 2005 Passat highline estate non runner in the hope to get it going, put it back on the road and use it as my daily driver. It's an AWX 130 pd 5 speed.

First issue was hard to start cold - glow plugs sorted that.

Scanned with VCDS and two faults.
01177 - engine control unit not currently testable.
This code clears but reappears when the ignition is switched off and the car is started again.

19466 Relay for fuel cooling pump (j445) p3010-35-10 open or short circuit to ground. This code does not clear.

I've looked and my car has no fuel cooling pump and I can't find a fuel cooling pump relay. The only fuel pump present is the intank pump and it is working fine (I've checked at the outlet of the fuel filter and fuel pumps out when the ignition is switched on).

The car now starts fine and idles without issue but once it warms up acrid white smoke starts to appear. It's definitely unburnt fuel in the exhaust as it stings my eyes so I'm guessing the cam lobes could be worn or I have worn injectors. Timing checked and is as good as I can get it (fluctuating between 0 and 1.2 on synchro angle in group 4 on VCDS)

The strange thing is I can stop and restart the engine fine right up to normal operating temp (80 degrees). If I stop the engine after it reaches 80 degrees or more it is difficult to start and when it does it idles for around 2 seconds with no throttle response and then dies again every time. I think the ECU is causing this as I've unplugged the coolant temp sensor and the car restarts and revs fine when up to temp, if I then plug the temp sensor back in and stop the engine it's back to poor starting, idling for a couple of seconds and then the engine stops.

I thought I'd check the ECU and the plugs underneath for the common water damage. Everything is good at both sides of the car (ECU side and comfort module side). However when I opened the box for the ECU my heart sank. Written on the ECU in black marker "ECU replaced March 2018".

Is there any way to find out if I have the wrong ECU? Can it be checked through VW with the vin number? The ECU currently installed is Bosch 038 906 019 ER.

Any help greatly appreciated.

Thanks,

Iain