I had the same issue, this is a problem with the iPhone 7 modem when updated. I had to take mine to apple to get it repaired. I’ll link the article below. They will repair it for free. https://www.apple.com/support/iphone-7-no-service/other-countries/
You might have damaged the motherboard in this while changing the screen. Were you grounded properly? I would suggest checking all the connections on the motherboard itself and unplugging and plugging everything back in. I'm almost fairly certain its something with the motherboard.
Water damage indicator is on the back cover of the tab close to connector. (a small square sticker (5x5mm) - its visible on ifixit last picture. Openig was much easier than expected - with a lot of patience SAFE. (I am not responsible for damage you do ... its just description how I did open mine) You need #0 Y screwdriver. 1 plastick knife (I sugest get something better as pry tool.) 1 old credit card (cut it in about 3-5mm stripes) 1 needle
I would suggest changing out the car fuse if you know which one is for the instrument panel and see if that makes a difference, if it does then go ahead and change the rest. If that doesn't do the trick then it might be something else. Maybe the battery?
I would suggest unplugging it and plug it back in again, I've had that issue before where it was unresponsive or there were some white lines going through. Usually that does the trick. If the previous screen is working fine and the new one is having issue then we know where the problem lays.
Hello, I found a useful article that explains the causes and 6 possible ways to fix this issue. It might be worth trying them, one one them has to work. See below. http://www.unlockboot.com/2015/09/6-ways-to-fix-itunes-error-53-when.html