So, I got my phone back a few weeks ago and it was my fault all along. Apparently some metal thingi got stuck at the bottom of the USB port and the tech had to dig that out. Their best guess is that it came from a USB cable. I checked the fxtec cable, which was fine, and two cabls I tried after the phone wouldn't connect anymore. None of them have damages I can detect - then again, I didn't find that metal piece either.
Advice to anyone having a similar problem: Be thorough when checking the USB port.