Are you the original owner of the phone and has it always been on this carrier?
Did you update the operting sytem or do a restore before trying the new sim?
Are you by any chance attempting to use a different network for the same carrier, for instance, switching between the GSM and CDMA side?
What message appears on the screen when you try to use the new sim?
Do you know if the new sim works in a different phone?
Have you contacted Apple Support to determine the current activation policy on the phone?