It would be worth in the first instance checking the cable from the LCD to the main board is attached properly at both ends, if it is you will need a new LCD [as long as the digitiser itself isn't cracked]
The LCD/screen itself is the same for the wi-fi and 3g versions, it is just the digitiser that is different between the two with the 3g version having an additional antenna for the 3g.
hope you get it sorted