Is it possible to replace only the LCD portion of the screen?

I dropped my phone a while back and cracked the screen. However, just today the screen started glitching and stripes covered the entire screen. The screen is completely unreadable and I can't see anything on it. Before all of this happened, the phone died, so I plugged it in. When I pressed the on button to show the low battery symbol, the screen began to glitch. I haven't dropped it in water or anything like that. I'm 16 and my parents already know about the cracked screen, however, if they knew I had damaged the lcd portion of the screen as well, they would probably disown me. Their punishment for the cracked screen was that I couldn't get it fixed and I just had to wait until they bought me a new one. I don't want to replace the cracked glass with an uncracked one because my parents would notice and probably get angry. Is there anyway I can just replace the lcd and keep the cracked glass?