Are you capable of receiving new sms? Do new SMS messages pop up?
If you're using the default or stock messaging app, try installing another app like Handcent or GoSMS and see if the same behaviour is repeated.
Else, try clearing all the messages stored and see. Within the default messaging app, there's an option to specify the Message Centre number - you need to verify that the number entered is what your service provider has assigned.
If that doesn't result in any improvement, see if a Factory Reset will help. Beware that a Factory Reset will erase all user data.