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There are a few things to check. Issue with SIM card or network can cause this. First test this SIM card with another phone. Is it working ?
If so, then either it is the network or your phone. Call the customer care of network and make sure everything is OK on their side. Sometimes they may need to register or provision on their side.
If the network is OK, then lets troubleshoot the phone. Go to Setting > Date & Time. Turn on Automatic Date and time. If it is turned on already, turn it off and set correct time manually. Turn off the phone. Take out the SIM card. Wait 2 minutes, put the SIM card back and turn it back on. Try sending a message to yourself. Are you getting it ?
Please let me know if that didn't work, so we can continue troubleshooting.