First thing I would do is to try the SIM in another phone to make sure it works. If it doesn't work in another phone, you'll have to get a new SIM. If it does, then I'd suggest a factory reset. It would be a pain in the rump, because you'd have to re-setup your phone from scratch (and if you do go that route, make sure you back everything up off the phone that you want to keep).
If that doesn't work, you may have a bad radio, which means sending the phone in for repair.