This was the case again (but not knowing the cause for the deep-discharging). At least the charging light blinked – as described here:
Fortsetzung der Diskussion von 
A little Guide to … Fairphone's Batteries (FP1 & FP2):
To kickstart the battery: Take out the battery of the phone; Wait for half an hour and put the battery back in the phone; Connect the Fairphone to a charger; If the charging light is blinking, it means that the battery was totally empty, wait for some minutes until the red light becomes fixed; A loading battery icon should appear for a few seconds (a short press on the power button will display it);
But instead of a fixed red light only the well-known 
fast-boot screen appears – and not the battery gets hot, but the area of the lettering “yours to open …” = the area of the motherboard? Found this related to FP1:
Ah, after some minutes in the described “fast-boot loading mode” and still “trying” to charge, my phone just vibrated once for half of a second – what does this mean?
Yesterday I was still able to boot into recovery mode starting automatically TWRP – ah, suddenly, after unplugging the usb cable and pressing the power button, TWRP started again… Battery level: 19%, CPU 56°C.
Next trials:
Restarting into recovery mode (within/from TWRP), but with inserted sd card (with the FP OS zip file) and plugged-in usb cable: Battery: “19%+”.
Installing seems to be ok – rebooting of TWRP and rebooting a second time, but now into “System” → oh no, TWRP appears again 
Only success: it seems to be possible charging the battery. now “31%+”.
Conclusion: maybe more than one part is defect of my FP2, bought: 2016-01-12.
The support answered some days ago:
“(Fairphone)” schrieb (Sa, 18.03.2017, 17.09 Uhr):
Since the Fairphone is not covered by the manufacturing warranty
https://fairphone.zendesk.com/hc/en-us/sections/200278526-Warranty
anymore, we advise you to go to a local repair shop and see if they
can open up the phone and clean out the corrosion.You can also send in your phone for repairs, our technicians will
then take a look and see if they can fix your phone. Fairphone 2
repair price list and FAQ
https://fairphone.zendesk.com/hc/en-us/articles/211437743-Fairphone-2-repair-price-list-and-FAQ.
Additional information is to find in our Return Policy
https://fairphone.zendesk.com/hc/en-us/articles/208223746-Our-Return-Policy-English-
Therefore this would be my last trial – sending it to the Netherlands…
… but no FP, no fun