I'm getting a message saying SIM card is full. Delete messages to make more space. When I tap on that it says no messages on the sim card. Any ideas on how to fix this?
Assuming you tried battery pull and reseating SIM?
Go into your contacts (People) and see where there are stored, click the the "Phonebook" at the top to see where the contacts are being stored, it should say about 6 in SIM which is the default Verizon numbers, if there are lots more you will need to move them from the SIM to Google (preferably) by tapping the menu button in people and selecting "Move contacts" and following the prompts.
Other than that, the SIM pretty much only holds SMS and contacts, if you are still having problems a call to VZW tech support might be in order.