[XPS 13] AC Adapter not recognized -> Battery not charging

My research has shown that this is a somewhat common problem. All of the sudden the battery stopped charging and the official dell AC Adapter, that shipped with the laptop, is listed as Unknown in the BIOS. I understand this happens because somewhere on the way the info from the pin that (for no good reason) identifies the AC adapter does not reach the charging circuit. This is supposed to be a safety mechanism (that no other manufacturer uses) that is obviously just an attack on off-brand chargers .The laptop is working fine (except for charging) as long as the AC adapter is connected.

What I did so far:

1. notice I'm out of warranty 
2. try different power outlets
3. try different AC adapter
4. Check battery health (it's fine)
5. replace Power Jack
6. Voodoo

It's still not working and I'm out of ideas.

Please don't tell me I have to throw away a 1300$ laptop because they designed this stupid point of failure into the charging circuit.