I'm using iPhone 5 with iOS 7.1.2 (11D257) on the UK O2 network and this problem is exactly as Peytons has described. It will work again briefly after either resetting the network or restarting the phone (muddled screen graphics always appear). I have been to see Apple Genius Bar on three separate occasions. They treated my problem as if I were the only user with an issue. Clearly from the list of posts I've seen there are lots of users with this problem.
The first time they blamed the carrier and provided a new SIM card. That didn't solve the problem.
The second time they reset the phone (pain in the backside) which solved it for only a few days.
The third time they said it was a faulty hardware in the phone (now 21 months old) and suggested I return it to Carphone Warehouse for a replacement,
WIth all kinds of users reporting this problem across all carriers in different countries it must either be a software or hardware fault. My experience is that Apple will not accept their responsibility and put this right quickly. Theyr're ducking and diving and that must be due to the potential cost of correcting this fault.
we'll to see what happens with iOS88