Multiple issues after screen replacement

Hi, I had my z3 screen replaced the other day, I got it back the next day and was delighted at the screen, it was perfectly fine. I got the phone home (stupidly didn't test in the shop) and popped my sim in, and had no service for about an hour, despite going all over my house.
So I took my phone back and they said they had to replace a part, so I received my phone back with signal, then the top of the screen had a very faded flickering, it was like a inner glow. I took it back and they had it for another day, I got the phone back to zero signal coverage, and now I can actually see the screen coming away on the left hand side (it's actually not flush with the case)

So I need somebody who is basically a mobile engineer to help me troubleshoot the problem so I'm more armed when I go in next, because obviously my phone was perfectly fine prior to the cracked screen repair.

Thanks for the help guys!
Jake