I hope my reply can help you even if your post is a bit old now!
It happens the same to me. The USB connector did not work anymore and it charged only in that position.
I’ve opened the phone and discovered that the PCB tracks soldered to the three central USB pins were broken (but you can still have some contact pushing the pins downward pushing the connector like you did).
I solved this way (with the help of a professional microscope and the help of my solder-wizard Fabio M.:
We have:
- removed the connector by unsoldering the remaining two lateral pins and the four ground pins.
- Cleaned the PCB from soldering tin
- I ordered a new USB connector from Farnell (the old one was probably usable but I preferred to buy a new one for less that 2 euros)
- the old PCB tracks were not usable anymore so he has soldered three small wires on the central pins and then soldered them to the three resistors to the left of the connector (see picture).
- remount everything and I got it! My Fairphone was back!