Worth a try: As you have already fastened the screws, also have a look at the seam between display module and core module. If you spot any gaps (on the phone’s slim sides), gently press the two together to close the gaps. This might help to fully restore the connection.
Regarding the charging issue, the most obvious suspects you could check are the battery and the bottom module (includes the charging port). If you know another FP3 owner or if there is a Fairphone Angel nearby, they might allow you to try another battery and/or bottom module in your phone, or yours in theirs.