iPod 80GB Classic won't mount (just flashes Apple logo), works only with wall charger

[gizmonaut]

Figured someone would see this and instantly know what the problem is (and yeah, I tried to search this forum for these symptoms).
Was given an "old" 80GB Classic (reads "2007" on the case). It works fine when plugged into the wall charger, but is dead when unplugged.
When connected via USB to my Macbook, it won't mount. It just flashes, weakly, the Apple logo.
I'd like to know the probable cause of the the malfunction before I send it off to be repaired.
Also, who performs the cheapest repairs stateside? I'm in Alaska, which usually raises the shipping rate.
Many, many thanks to the person who saves me a buck or two with a diagnosis or other advice...

 

[rgarjr]

if it works fine with the charger plugged, and not without it, then it could be the internal battery.

 

[pkorisa]

80 GB Classic

I agree with the previous note that the internal battery has gone bad and must be replaced. This si why it does not keep charge and why nothing else works. Find the cheapest place you can someone replace the battery.