Passat Automatic Transmission Not Shifting - No Errors?

Hi,
Today, I attempted a diagnostic check on a Passat V6 TDI 4M (year 2001).
While the car can be put into gear, there is no power being delivered. Only after a period of warm-up does it produce a slight amount of power, but also a smell of burning/grinding if you push it too hard.

I initially noted down the following errors (engine 17978, likely just a previous battery issue) and (transmission 17125, torque converter without lock-up), then I cleared them. I then started the engine and waited for new errors to appear, but nothing came up! Nevertheless, the car won't move. The display indicates that the gears are being shifted, and this is also recognized by Mercedes, and the voltage is 14.2V.

First of all, here are my thoughts on the matter:
"No sensor errors are detected, there is no electrical interruption, and the display also shows no red digits (indicating an emergency mode). The transmission error 17125 only indicates that the engine and transmission speeds were implausible, which is understandable given the lack of power transmission."

There were some previous issues with shifting (-> is an oil change necessary/advisable?!), but no noticeable problems in curves, etc. (-> oil level is probably okay?!). Now, the car is sluggish after having been parked for several weeks in very cold temperatures and only driven short distances occasionally.

I now suspect a purely hydraulic problem. Since there is no pressure build-up, either the torque converter is not being supplied with pressure, or it is leaking, or a gear/brake band is not being engaged. Perhaps a valve is simply stuck.

Now, here are the questions for you .
-What is the best way to check the hydraulic pump and valves?
-In which measurement blocks (MBs) should one search, and where will meaningful readings be provided?
-What explanation is there for the fact that no new errors are being displayed?

Thank you and greetings.
carsten

First, I would check the oil level as soon as possible. If it smells burnt, the clutch packs are likely damaged. Take a look in the search; we recently had a similar issue with a Passat, where there was a significant oil leak from the transmission. I suspect that's where your problem lies.

Here it is:
Okay, I understand. Please provide the German text you want me to translate into English. I will only provide the translation.

The link works perfectly, thank you.

My recommendation was to first bring the car into a warm room (it's still around -15°C at night here) and see if it becomes drivable. If it does, then warm it up and do an oil change. However, as described in the link, it's probably more sensible and cost-effective to first top up the fluids and check for leaks.

One possible explanation for the lack of errors would be that the hydraulics in the slide case are not causing any movement, and therefore, despite the CAN display showing a desired idle state, the system is actually idling as intended.

Does anyone have information on which pressure values can be read out? Surely, it should be possible to check whether the pump actually builds up pressure and whether the two valves for flow control are working...