But no cellular signal

Is possible the motherboard has been damaged during the screen repair. I have seen this happen many many times on the iPhone 5/5s/5c. Where the screw driver or pry tool slips while removing the screws or prying the batt / screen connectors.

It's also possible the screws for the screen have been put back wrong. For example if a long screw was put in position of a short one, then it's possible it has gone down far enough to scrap against the mother board and cause this issue.

You mentioned the antenna. This shouldn't really have been touched during a screen repair but not going to rule it out. However i have found with some iPhone 5's with this issue that changing the antenna had no effect. Bringing it back to a board issue.

If it's a board level repair it maybe very costly.

Hope this helps