Clayton Little did you try to connect it with Firewire connection instead USB? The 3rd gen can only sync via USB and not fully charge. It does however sync and charge via Firewire support. Best bet to get it going is by ensuring you have a known good battery and that you use a Firewire connection to see if that works. It needs to be connected to a FireWire port to work reliably and charge at the same time. It is designed to be connected to FireWire (not USB) using the included FireWire docking cable. If you are connecting it to a USB port, that may explain the problems.
You can always try the diagnostics mode as described on here to see if it gives you any error.
As a sidebar, I love the sound that comes out of my 3rd gen. Prefer it over anybody's new iPhone:-)