Follow the steps below for a full diagnostic.
1) the first thing that should be done ever, is to Check the IMEI with the national blacklist. verify that it has not been reported lost or stolen.
2) Test with another active SIM, and verify it isnt an SP issue (We had 4 iphones come back the same day once, because Roger network was up when they dropped their phones off, then down when they picked up the phones.)
3) Run a Networks Settings Reset
4) next move on to replacing the part back to the original. It is not LIKELY that the screen is causing an issue, but i have seen weirder things happen to devices.
5) Be sure to check for any loose connections on the board. (the antenna may have been sitting loose on the board, and shifted off of its connector
6) After this, try replacing the cellular antennas on the device. see if that fixes the issue.
7) Scan the board for physical damage. (a missing resister, or damage to connectors)
8) Next, a factory reset. make sure there isnt a software corruption
After all of this has been done, the problem is likely ESD from the drivers or other tools, in which case a Logic board replacement is needed