How do I get my phone to connect to the cellular network?

A couple days ago, my 4S started randomly rebooting whenever I moved the phone at all. After about a day of this, my phone stopped being able to connect to the cell network, and it instead says "Searching..." A couple days later I finally had time to open it up and I found two screws completely unscrewed. I fixed all that, and then the phone no longer rebooted itself, but the "Searching..." problem remained. I've tried all the other solutions to this common problem like taking the SIM out or manually setting the date, but no matter what I do it always says "Searching..." at the top. What I'm wondering is if the constant rebooting (often times during the boot-up process) could have harmed the cellular antenna. If so, will a restore from backup fix that, or will I need to replace the antenna completely? If it helps, on my "About" page in the settings, I see no IMEI number and the Modem Firmware section is blank. Also, I'm on Verizon, if that makes any difference. Thanks!