First, you can't backup via the PC but you can via WiFi. Your phone works fine with WiFi I hope. You can copy out videos, docs and photos via PC, which I would recommend doing anyway.
Next, it could be your SIM causing the issue. It's not unheard of. When my wife and I got back from Morocco she had no cellular connection at all. It was the SIM card, got a new one and everything was fine.
Lastly, you can use this program to revert to WP8 before sending it in for warranty.
FAQ - FAQ - How can I recover/reset/restore my phone software? - Nokia - UK
You will need to backup prior to using that program as it wipes everything clean.