How can I fix my cracked screen on my cell phone?

I have an LG Ally and I recently dropped it and the screen cracked beyond belief. I used the insurance and paid the 89 bucks through Asurion from Verizon for a replacement. Basically, I was wondering, what if I pulled the pieces of gl out one buy one. would the touch screed still work? Also, why don't these companys use a clear polycarbonate face or plexi gl face. Does gl work better for the touch screen to work?