Top 1/4th of screen unresponsive.. hardware or software problem?

I dropped my phone in a thin carpeted elevator. It landed on it's back and really didnt appear to have any damage at all. It wasn't until later that I realized the top 1/4th of my screen is totally unresponsive (from status/notification bar area down to where the google toolbar widget is located by default). I also noticed from time to time it will randomly select things like there's 1000 fingers touching the screen at the same time. It totally freaks out. It will jump around, type random letters in texts, and swap home screens on its on. But it doesn't respond to touch at all on the top of the screen. Also, if I squeeze the sides of the phone, like to put the back on, it will act like someone is touching the exact center of the screen. If keyboard is up when I grip the sides, it will type tttttt which is near the center. So, I did a factory reset twice, and did it again by doing the fast boot and android recovery. It didn't help at all. Should I replace the screen, or even take it apart and put back together to see if it just knocked something loose? I've replaced an iphone screen before, I'm confident I could figure it out. Thanks!