I've been to my network provider and the problem is with my phone. I woke up on Tuesday with an unread message but have been unable to respond since. My lock screen says that I can make "Emergency calls only", but shows full network coverage.
I have CM7 on the phone, and tried a new install last night to no avail. I did spill some water on the phone about two weeks ago, but the phone has been working fine since. Most confusing is I received the text above at 08.00 and the problem has been present since at least 10.00 on the same day.
Any advice is welcome. Samsung Galaxy S2