1st Gen iPod stops charging when picked up

[JCLrox]

I have a 2001 first gen iPod, and I have noticed that if I pick up the iPod while it is plugged into the wall, it stops charging. If I pick it up while it is plugged into the computer, it restarts. Another possibly related problem is that the iPod will not charge unless I keep my hand firmly pressed against the charging brick when it is plugged into the wall. It usually stops charging if I move my hand. Could this be a faulty Firewire port on the iPod? Or perhaps the charging cable is on its way out?