Can I fix my iPod?

I have an iPod mini (one of the newer, short, fat ones) and it broke on me while running the other day. I had it stuffed into the elastic of my shorts and I guess it either overheated or got too much moisture from my sweat. In any case, I took it out after about 3 miles and the music was still playing, the screen was glowing, but completely blank. Now, it just doesn’t seem to work at all.

Any suggestions?