I don’t know if this issue is still actual but for the record I’m adding some points I observed.
My FP2 got stuck in a Bootloop after upgrading to Android 6 Marshmallow (Bootloop Android6 Marshmallow), but before I found this post I observed some similiar behaviour of my FP like you described:
- when I remove the battery and plug the phone to my PC, then the “powered by Android” screen appears and a short vibrating every 2 seconds, with short blinks of the red LED
- when I remove the battery and plug the phone to my standard-charger, then the screen does not appear, but every 6 seconds a short vibrating, with red LED
- when I insert the battery while the phone is already plugged in, then the phone boots (or it tried to, in my case)
- battery inserted and afterwards plugging in leads to normal charging, without booting
So this post is not really related to your problem, but maybe it helps somehow. After my observations I would have said maybe you have to replace your battery, but you already tried that…