WUUUUUHUUUUUUUU!!! 
It just works again! Well I tried a different recharging-unit and tried Alfi’s tipp again and instead of stopping to recharge after 5 min, it just continued to recharge. After some hours, it was completely recharged. So I started it (without the cable plugged in).
And what happened after I booted Android and plugged in the USB-charger? Right, it just worked again, like it should. The symbol in android changed and the LED switched on.
So I guess my theory about some strange config-state in android, caused by some odd combination of commands sent by windows and/or apps could be still possible.
What helped? I guess (I’m definately not sure!!!): an empty battery and Alfi’s tipp.
I hope this can help someone in the future. For now, I’m just happy not to file a support request and keep on telling everyone how great and magically my FP2 is! 