Ok, so after charging the battery, it seems that the Phaeton is satisfied

The currents are about 13.8V on the battery, aswell as on the analogue dash readout.
The problem with the trunk remains though

It doesnt respond to either command - press on VW emblem, remote open, or the one in the drivers door. Only the turn signals flash. When I open it with the key, and want to close it - no response to the close button.
I found a thread, where people say, that the trunk can behave strangely when something is not right. I tried all possible combinations, still no luck.
Any suggestions? Expoman does your trunk work now?
Thanks