I've fixed a few of these and it sounds most likely that you will need to replace the LCD screen. However there is no harm in checking over the connection and doing a hard reset first. If its still not working you can find get an iPhone 3G Screen Replacement and this will fix your issue.
Glad to hear I'm not the only one to damage the iPhone 5 so quickly!! I got my screen on Saturday from RepairsUniverse here - iPhone 5 Screen. It arrived yesterday and my iPhone is now like new again. Got the case too so hopefully it will last longer 2nd time round :)