Locate your hosts file, in Mac OS X this is /etc/hosts and in Windows this is c:\windows\syst
Open the hosts file with Administrator privileges
Add the following lines to the very bottom of the hosts file:
(should this line already be in your host file, follow the link that Ryan provided about an answer by Majesty, it will work especially if it is jailbroken) I will tell you to delete this line as well as other lines that reference to gs.apple.com
Connect your iPhone to the computer
Put the iPhone into DFU mode by turning the phone off and then holding down the sleep and power button for 10 seconds, then release the power button but hold onto the home button until iTunes tells you that the device is now in recover mode"
Restore your phone with a new firmware and not your saved one. I personally would suggest you download custom firmware from here On top of his page, it will tell you how to use it. I would also stay away from the newest firmware for now. You could use 4.3.5/8L1. hope this will work for you. For now, do not worry to much about your LCD since it may be a. firmware issue or b. a separate error that could be resolved with a new LCD. Good Luck and let us know what happens.
Unless you are a skilled electrical engineer with state of the art equipment and vast knowledge of the inner workings of the iPhone 4 mobo, there's not a chance that you'll actually be able to repair it. Your best bet is to see if they're for sale somewhere online, or just get a new phone..