I shut off my Note 3 and pulled the battery then pulled the Micro SD card and lastly I pulled the SIM Card. Someone had suggested that they had reseated their SIM card and it helped with the poor reception on their Note 3. I put the SIM card back in and then the Micro SD and the battery. I booted the phone back up and now it says "No SIM Card" and I have no service whatsoever. I have tried rebooting and re-seating the card many times and still the same error. Are SIM cards that delicate that it was damaged just by pulling it out? I did have to put a little force on it to get it to slide out because of the crappy design of the slot. Do I basically have to take it in to get a new SIM card at this point?
I just put the SIM card from my old Note 2 that my son is using now and it worked fine and then I put my SIM card in the Note 2 and it said "No SIM Card" so obviously the card is bad. I guess it must have been a crappy card to begin with for it to go bad just by pulling it out. The SIM card from the Note 2 is just fine after pulling it out and putting it in my Note 3 and then pulling it out again and putting it back in the Note 2.
SIM cards can go bad, they also can be damaged if you touch the gold contacts. And yes, removing one from a Note 3 can be a pain. Sounds like you need a new SIM card; they're free at your local Corporate Verizon store.