My Galaxy S3 would intermittently (once or twice a day) lose the cell signal.
Being optimistic, I ordered your tools and tried to find the problem. I opened the phone and removed the first inner plate, and the shield on the SIM card fell out into my hand!
I wedged it back into its clips, put the screws back in, and the phone has worked ever since!
Don't be afraid to open a modern device. Sometimes it is not working for a trivial reason!