If it was just phone calls I'd suggest checking your call divert settings, but messages not arriving as well is odd. I assume you've tried rebooting and toggling airplane mode on and off.
I'd speak to your carrier, to see whether there is a problem at their end. Also if you could try a different SIM in the handset (assuming you are not a CDMA user) or try your SIM in a different phone - if the problem moves with the SIM then either the SIM is faulty or it's a problem with the network or account.