TDI 2.0 16V BMN, severe idling issues

After investing a lot of money and time in my Touran (2.0 TDI, 16V, 170 hp, BMN) and being unable to resolve the issue, I'm trying to find a solution through this platform.

Briefly, regarding the history:
- The timing belt skips a tooth after the broken serpentine belt has wrapped around the crankshaft pulley.
- Valves, hydraulic lifters, and rocker arms are damaged or broken.
- A refurbished and tested cylinder head (with a 1-year warranty), including valves and camshafts, will be installed.
- The rocker arm shaft and PD (pressure distribution) elements are taken from the "old" cylinder head.
- New sealing sets for pressure-differential elements, including adjustment screws, as well as wiring harnesses for pressure-differential elements and glow plugs, will also be installed.
- PD elements are adjusted according to Volkswagen's instructions.

Since this action, the engine has been running roughly at idle, especially when warm. The idle air control system shows a maximum value of +3.89 mg/H on cylinder 4. On average, this cylinder should be around 2 mg/H. Under full load, in the 5th or 6th gear... Strong vibrations and a lack of power are occurring, which, in my opinion, are due to the PD elements.
The error code "004713 - Valve for pump/injector, cylinder 4 (N243)" and "P1269 - 006 - Implausible signal - Intermittent" are repeatedly being stored in the fault memory.

I have already swapped the PD elements (presumably referring to piezoelectric elements or similar) from cylinder 1 and cylinder 4, but it didn't resolve the issue. A compression test was already performed at a specialized workshop and yielded very good results.

I would appreciate it if someone had another suggestion about where I might be able to start.

Following the limited response I received, I'll try to come up with some possible approaches myself.
Could the problem possibly be related to incorrect valve timing? Would replacing the timing belt help? According to VCDS, the crankshaft position error is 1.49° after top dead center. The tolerance is +/- 1.5 degrees.
Could a control unit update potentially resolve the issue?
"Are there possibly..." Is the bearing on the connecting rod or the rocker arm shaft damaged?

Hello.

Quote:

The error code "004713 - Valve for pump/injector cylinder 4 (N243), P1269 - 006 - Implausible signal - Intermittent" is repeatedly stored in the fault memory. I have already cross-swapped the PD elements of cylinder 1 and 4, but without success.

Then, the only possibilities left are a wiring harness issue or mechanical damage to the affected cylinder.

Best regards, Rainer.

major wrote:

Briefly, regarding the history: - The timing belt skips a tooth after the broken serpentine belt has wrapped around the crankshaft pulley. - Valves, hydraulic lifters, and rocker arms are damaged or broken. - on cylinder 4, a maximum of +3.89 mg/H. On average,

Hello...

"Maybe the connecting rod took a real hit, and you're simply experiencing low compression in that particular cylinder..."
Is he trying to compensate for this with excessive injections?
I actually thought the value should be around ±2.9 mg/dose.

My next step would be to check the compression... what were the results? Saying "very good" is vague when we're looking for a precise value.

Was the pressure loss test for the valves also performed?

Does the car perhaps have any "flaps" or valves in the intake passages?


SG
Manfred.

I initially had a BKC (presumably a medical abbreviation) related to "oil splash."
The affected cylinder had a pressure 10 bar lower than the best intact one.

Since I tried using "Ultimate Diesel" as fuel, the engine runs more smoothly. The irregular idle only occurs occasionally when the engine is warm. The only thing that's disturbing is the strong vibrations that start at speeds above 130 km/h.
Therefore, in my opinion, damaged connecting rods are rather unlikely.
The compression ratio is approximately 30 bar for all four cylinders.

I'm now suspecting that at least one of the PDEs comes from Siemens. It's clear that the cross-linking of cylinders 4 and 1 wasn't ideal, as both cylinders were trying to compensate for each other.
At this point, I will start again.