Phone says no sim card installed after screen replacement

EDIT: Now I've reset it, and I can't get in at all! It says "SIM required" on setup.

After replacing the screen on my iPhone 4 for the second time (The first repair didn't last long), the repair was relatively successful with (most) functions working properly. However, after booting up my phone, I find it does not recognize the SIM card. I have tried inserting the sim card from my sister's phone (which is identical) with no luck. It seems it is unable to read the sim card.

My best guess is that it is caused by some of my screws being missing. Some are missing from sending it to a repair shop where the phone was reassembled with missing screws and some screws just loose inside the phone.

My phone is missing several screws. It is on its third owner from my family, and has been broken a total of 3 times. The first time, we had it sent away to be fixed. Whoever did it did not do a careful job. When it broke under my ownership, I decided to fix it myself, to discover several screws loose inside the phone, as well as several screws missing. The only screw different from my last repair to this one AFAIK is the center display screw on the battery side.

Should I try this, or a factory reset? How is it best to proceed?

P.S.

I have a full set of iPhone 4 screws to be delivered to my house Thursday, but it is vastly preferable for me to have a functional phone during the weekdays.