iPhone stuck on activation screen and is only saying 'NO SIM'

Please insure that your SIM card is oriented and installed properly. I know it sounds like a dumb suggestion but this stuff does happen. It is also possible that your SIM card is simply defective; can you try someone else's SIM card to eliminate that possibility? If a known-good SIM card (appropriate for your phone as it may be carrier locked) doesn't work, then...

This brings me to the third option and that is it could be the SIM Card Reader which is defective. It is possible that one of the internal pins is bent or shorting to an adjacent pin. You could open up the phone to take a look. Follow this guide. If it is just a bent pin, you should be able to fix that. If the pin is broken, then that will require a micro-soldering repair.