iPod Classic Doesn't Charge in PC Port

This is my first post, so bear with me.

So, I'm at school, and a 4th grade teacher calls me down to her room. She said she had two broken iPods w/ chargers. She gave these to me, saying that I could keep one if I could fix them. She wasn't very good with technology, and I simply charged the iPods and they turned on and operated. Except for one. I can use the second iPod if it's plugged into the wall and stand for it, but If I plug it into my PC, it shows the Apple logo and quickly turns off. Both iPods are 1st Generation 40GB iPod Classics. It doesn't appear in the iTunes window, so I can't update/restore it. Any help?

-Ben