1st Generation iPod Won't Turn On

I have a original 1st generation iPod. Yes, the one with the scroll wheel and 5gb (wow!) drive. It doesn't turn on though. Originally, I suspected a loose connection from the battery to the logic board, but testing with my multimeter shows me the connection is fine. The iPod doesn't turn on at all. I tried plugging it into my computer's firewire port and pressing the menu and play/pause button to no avail.

I have a picture in this post of the iPod - all dead like a brick. Do any of you have any suggestions? I am at a brick wall right now and need to find some solution. Or if any of you know where I can get the iPod repaired or get a cheap logic board replacement? I can't spend too much though.

Thanks.