My iPod Touch 4G's screen has gone white and has lines on the screen. How do I fix it? Help!

Hello everyone,

I've had an iPod Touch 4th generation for a few years now, and, today, for the first time, the screen has gone white and their are vertical lines on it. What happened was I accidentally dropped my iPod Touch on tile and it landed on its back. I tried it out right afterwards to see if it was still working and it seemed like it was perfectly fine. Later on, I got an email from one of my friends, so I slid the email button on the lock screen to see the email. In the email, there was a link to a gif image, so I opened it in Safari. After I was done with it, I closed that tab. I also had a second tab open from earlier, so I wanted to close that tab as well. When I clicked on the button to see all tabs and close one, the screen completely froze. I held on to the on/off button on the top of the iPod, and, after about a minute, the screen switched to a completely white screen with lines on it. I've tried holding onto the on/off button again and it doesn't work. I also tried plugging it into my Windows 7 computer and opening iTunes, but my computer doesn't even recognized it is plugged in. It won't appear under the "computer" section in Windows Explorer, which will allow me to do USB-related tasks with it. iTunes doesn't recognize that it is plugged in either, so I can't do anything like restore the iPod to factory settings. The home button on my iPod hasn't been working for a while so i've always been using the accessibility feature that gives me a home button on the screen. Now that I can't access that, I can't hold down both the on/off button and the home button at the same time. What should I do? Should I send it in to Apple for repairs (which I won't do and would rather buy a new iPod Touch)? I am thinking of just leaving it to, hopefully, have the battery drain and the iPod would die. Then, I could charge it and see what happens. Other than that, i'm just clueless right now and I have no idea what I should do. Please help me!

My iPod Touch is an iPod Touch 4th generation model with 8GB. It is running iOS 5.1.1.