Please insert SIM emergency calls only
I bet I have more experience with this than anyone else with a Samsung Galaxy S4 for AT&T 16 GB
This hand set was run over by a large SUV and I was amazed it survived and kudos to otterbox.
Since then, I've been having this SIM error as well, at random. I see it reported that pulling the SIM out and putting it back in was the only thing that worked, I'm glad simply rebooting works for me, so I don't have to peel apart the otterbox all the time.
I tried the tape and it didn't fix it so I replaced the SIM/SD card tray. The new part on Amazon cost me $14 and the YouTube video showing the operation of peeling these things apart was helpful. I didn't see a video in particular about how they're glued down but I managed to peel the original SIM/SD card tray off, scrape off the adhesive that was still stuck on the motherboard, and install the new SIM/SD card tray.
I still get random SIM errors. No change. Putting a layer of tape on the SIM chip was easy, replacing the tray was difficult, and neither one of these efforts to fix it worked.
My SIM errors are the definition of random, I get one error right after another in just a few minutes, or it will stay lit up and working for hours.
So I put my wife's SIM card in there to make sure it wasn't the SIM itself making the problem. She's never had a problem with her SIM in her Note 2. Guess what, she let me use her SIM in my S4 and it wasn't very long and there it was again. "Please insert a valid SIM" emergency calls only. I gave her back her SIM as soon as I saw the error, as she was not happy about having the cover off the back of her Note 2. I did not get the error when I put my SIM into her Note 2, but was not able to test it for very long, as I got the error on my S4 with her chip so soon.
Next I am going to peel it apart as thoroughly as I can and look for any connector plug that can be unplugged and snapped back in. There was only one little ribbon with a 24 pin connector from the new tray to the motherboard. I'll pull that off again too, and inspect it with a magnifying glass.
I will report if I am able to figure out how to fix this problem.
My wife thinks it's because I flash it, but I doubt returning to stock is even worth the effort. I've never heard of a ROM being the culprit.