While I can make no promises, it should fix the issue. Was the phone dropped, or did this randomly occur?
The LCD and glass digitizer are fused together, so when you replace one you will be replacing both. The flex cables that attach the LCD and digitizer to the motherboard are included with every new screen. However, you will need to buy new adhesive for the screen.
This is a good example of the tape (however, this is a more expensive five pack). The LCD can be purchased here, as iFixit does not sell parts for this phone. If you follow the instructions on iFixit and take your time, your phone should turn out fine.