Hi everyone,
Sorry for my english if I make mistakes, I'm french, and still learning even if my wife is english ;).
So I had the No service problem after replacing the LCD screen on an iPhone 4S and the Simcard seemed not to be recognized anymore. I checked everything I read in comments of differents questions about this problem people asked on iFixit.
Everyhting was connected correctly, I didn't break the litlle blue coil etc... After a long long night searching, I found where was the problem.
The little black pressure contact underneath the battery connector was not "high" enough. I don't really know if you gonna get what I try to explain but I try. This pressure contact has to touch the back cover of the iPhone where there's a metal part who's connected by the two screws to the external antennas of the iPhone. So I just put a little more up this part for that to touch the back cover when you close it.
In the end I recovered the signal and everything works well now.
I'll put some photos if any of you need some and hope that can help you! ;)