I had this same problem, but it wasn't due to a faulty sim.
My sim tray would not come out by inserting a paper clip or sim eject tool. I felt like it was going to break the phone. I finally managed to get the tray out and when putting it back in I got No Sim error.
Turns out the screw that holds the eject mechanism is loose inside the phone (you can see the screw rattling around inside the sim slot).
I put a piece of tape on the back of the sim / tray to hold it more firmly in the slot and it is working until the rush dies down and I can schedule a replacement.