UK Car Repair Questions? Ask a Mechanic for Answers ASAP
What year is your A4? And does the cluster display show what gear you have selected, or are they all highlighted? Engine starts and runs ok?
Does your transmission have the removable pan on the bottom, or on the front? If it is on the bottom, I would start out by checking the wiring connectors that are on the front of the transmission, see if they have fluid leaking through them into the wiring harness.
Do you have the Audi S-Tronic DSG transmission? (link to page and scroll down for identifying pictures)
You would have to replace it with the same transmission code
If you can find an HHE or other 01J style CVT transmission it should work, but you may have to get the ECM as well since there may be upgrades to some systems that would not be compliant with your ECM. As long as all the connectors are the same (which they should be if it is an 01J tranny) it should be fine.
A problem with the clutch is not going to solve your electrical problem- when you started out you had a fault, and all gears highlighted. I understand the clutch may be burned, but that may be as a result of the transmission failing electrically, not the other way around.