The easiest way to ensure this isn’t a problem is switching the Date and Time settings to ‘automatic’, which can then force the messaging apps to work.
When everything else fails, go right back to the beginning: take out the SIM card and start afresh.
Puzzled, I checked the settings on my i Phone, only to find both i Messages and Face Time were disconnected.
Well, technically, they were “waiting for activation,” the screen told me, but the end result was the same: they didn’t work.
Begin again with the process of setting up the new card, let the device recognize the number and check that i Messages and Face Time have started working. If you are staying in a particular country for a while and will have that SIM the entire time, you might want to restore your device through i Tunes with the new SIM card inserted.