Power down. Grab a sim removal tool, or a stout paperclip. Remove sim tray and reinsert. Power on and hope for the best. Next stop would be the carrier for a new sim, or apple store.
I had the same issue for the past 3 days. This morning, I went down to the local AT&T store for a replacement SIM card. They installed a new SIM card in some 5 minutes. Hopefully, this will resolve the "no SIM card installed" issue.
There appears to be quite a few people, whom are experiencing the same problem, over at the Apple Community site, as well.
Power down. Grab a sim removal tool, or a stout paperclip. Remove sim tray and reinsert. Power on and hope for the best. Next stop would be the carrier for a new sim, or apple store.
Go get a new SIM card from your carrier, no big deal. As long as your screen isn't cracked or you dropped it in water, there isn't much to worry about.