In reply to FesteringSoreBugs
Problem: SIM card not recognized or no signal
A few people with the LTE version of the Nexus 7 (2013) have run into problems where the SIM card seems to stop working. This is usually accompanied by a “No SIM card” message. Sometimes they get the message “SIM card added” and a prompt to restart. For some people the network just seems to go missing and there’s no service, but they don’t get any message about the SIM card. Bear in mind that SIM cards from U.S. carriers will not necessarily work in European Nexus 7 tablets and vice versa because they may use different channels.
Potential solutions:
Try rebooting the Nexus 7 by holding down the Power button, ignore the prompts and wait for it to restart.
Try pulling down the notification shade and going into Airplane mode and then turn it off again.
Try turning the Nexus 7 off and removing the SIM card, make sure the card and tray are clean and then reinsert it before turning the tablet back on.
Check what your Access Point Name settings should be with your mobile service provider and then go to Settings > Wireless & networks > More > Mobile networks > Access Point Names and make sure they’re correct.
If you’re able to use another SIM card then test it in your Nexus 7 just to verify that it’s not a faulty SIM card.