I replaced the glass on my daughters siii shortly after we got it. We bought a new glass on ebay for about $25.00 if I remember correctly (colors are available). Remove the back cover and battery. Gently heat the broken screen with a hair dryer from about 6 inches. With the plastic tool supplied start pulling away the broken pieces, getting the first one away is the hardest. After all of the broken glass is off clean THOROUGHLY with lint free screen wipes. Now the new glass comes with a full size piece of double sided tape (for screen and/or borders) but I didn't want the chance of a bubble in the center of the screen so I chose just the border portion of the tape witch goes around the screen and above and below the home, back, and menu buttons. Carefully remove one side of the tape and apply to the phone. Make sure the back and menu buttons don't move around (mine did). Now peel off the remaining side of the tape. This is your last chance to make sure your screen is clean and dust free. Apply the new glass pressing firmly around the edges.
I did this about a year ago and haven't had a problem with touch response. Good luck.
