1) Wifi has nothing to do with phone service except the screen, the battery, etc. One can work perfectly and the other can be dead. They're two completely different radios. It's like the bedroom TV working but the living room TV doesn't turn on.
2) The SIM card socket in the S3 could have gotten damaged when you pulled out the old card. There could be something really flaky about the card. The S3 could have other problems. It has to go to a shop to be diagnosed, there are too many possibilities to even point you in the right direction if you were a trained electronic technician with no cellphone experience. This is a "let's see if ..." kind of repair.