Hi Jakob!
Hm that doesn’t sound good. Have you tried to dis- and reassemble the battery? Otherwise, I only have the following ideas:
Disclaimer: Only try the following, if you don’t mind losing all your data. Otherwise, my only suggestion would be to contact support (scroll down to the bottom of the site).
Do you have a backup of your data? If so or if you don’t mind loosing the data, you could try a hard reset, i.e. wipe data/factory and cache in the recovery menu (see step 2 in these instructions). Just to be sure, I mention it again: All your data will be lost after this!
If this doesn’t work, there is also a topic about a soft bricked FP2 (your phone is not “bricked” but at least also screwed up). The solution there is to flash a fresh copy (a zip file) of the OS via recovery, which will also erase all your data! However, I’m not familiar with the procedure there and can’t estimate how complicated this is.
Btw what do you mean by that? If you power on your phone with the power button, then the phone is in the mode of booting the OS. In this mode, there is no possibility for fastboot to be enabled. Fastboot mode is accessed after turning off the phone by pressing and holding the Volume Down and the power button for a few seconds. Note: in this mode you’ll only see a Fairphone logo and nothing else will happen.