Fairphone Support is experiencing some capacity issues, so they can take weeks to reply (unfortunately).
There are various reasons reported why the screen sometimes has a mind of its own, check out the first post of this topic for an overview:
To avoid the phone blocking the SIM card again, I’d try whether workarounds help without the SIM or SD card in the phone. If you solve the problem, you can put them back again.
You could also try whether removing the screen and reassembling the phone helps; there may be some useful tips here. Other than that, the quickest way to get support is by calling them (details at the bottom of the support pages), or ask here if you’ve been waiting a long time.