#1 There is a diagnostic in Itunes (under help, just follow the instructions) that will check for problems and things. If it fails to find an Ipod connected, this is likely your system board failing.
#2 There is also a built in diagnostic tool on the Ipod as well. First you'll need to do a hard reset. Press menu (up on the wheel) and select(center button) for ten seconds to do it. Then you have to get into the diagnostic. Just hold the center button (select) and the left side button (previous track) for ten seconds to access the diagnostic tool. if it still wont even get into this, it is likely your system board has failed.
#3 The hard drives on these are the heaviest component in the device, and not actually secured, physically, to anything inside the metal chassis Its just suspended, and held in place by a few rubber cushions and foam. Sometimes when they are dropped, the hard drive smacks against the two little transformers at the bottom of the main board on either side of the back of the dock port, and knocks them off (sometimes not completely off, but just hanging on by some adhesive). This may cause an intermittent connection between the system board and the transformers, and it may only have enough power to barely boot, since it doesn't have the full charging capacity, and its certainly not enough power to charge the battery.
Any of these things will only be solved by swapping the system board.
Swapping a system board in one of these is a tedious, but not impossible task (link on how to do it Link Removed), and will at least get you to the point where you can use the diagnostics to tell if something else is bad in the unit.
If you look on e-bay there are several shops that sell the replacement system boards for less than 70 bucks. I have a bag full of parts for these exact units (including harddrives and main boards), if you need some other parts, PM me and I can fix you up, or I'll trade some bass gear for services/parts, if money is an issue.
I did not know about any of this, but am glad I do now
