I have seen several reports of people having the exact same problem - although with the iPhone4. Their solution seems to have been either to
(a) Power the device down, remove the SIM card, power the device up, power the device down, insert the SIM card and power it on again.
(b) Reset and re-enter all the network settings.
If you've not already tried it, you might also try the iPad's 'fix all problems' cure of completely powering the device down (hold down the Power switch for a couple of seconds) and then powering it on again. It fixes a whole load of unexplained problems - a bit like rebooting your PC.
Let us know if this works - if not we'll try some more 'interesting' solutions...
Welcome to the Forum, by the way!!
Tim