Try powering down the tablet, removing the SIM card, then reinsert the SIM and restart the tablet to see if it can reconnect with the network. You can get a new SIM card free at a corporate Verizon store, as they can get corrupted.
Have them put the card in and test the tablet at the store to be sure this solves the problem. If it still won't connect tot he cellular network, perhaps they can do some troubleshooting in the store for you.
I'm assuming you've checked the Settings and ensured that mobile data is on? Have you tried turning off the tablet and removing the SIM card for a minute or two, then reinstalling it? If that doesn't help, you may need a new SIM card; they're free at your local Corporate VzW store or by contacting Customer Service.