Technically there was no iPod Classic 7th Gen. There were 2 revisions to the 6th Gen, and the difference is determined by capacity, color and features.
I see some places calling the 6th Gen revision1 as the 7th Gen, so this may be splitting hairs.
The 6th Gen (2007) was either 80GB or 160GB with a Black Front Plate and Wheel
The 6th Gen revision 1 (2008) replaced the 80GB with increase to 120GB and added Genius, it has a Grey Front Plate and Black Wheel
The 6th Gen revision 2 (2009) replaced the 160GB with a single platter drive, slightly lower battery life and added Genius it has a Grey Front Plate and Black Wheel
As for the USB Charging, I would be looking inside the USB Port for hair and debris of the iPod, and carefully cleaning it with rubbing alcohol and a plastic pick. If the charging wires are blocked by non-conductive material, that will stop the charging process but allow data through. The 30 pin connector can also have broken wires preventing the charging. It looks like pins 16 (Ground) and 23 (5V) are the ones used for power via USB.
If that doesn't work or you see broken wires in the connector, then you may need to open the iPod and replace the connector. It also is possible that the internal connections are broken inside the iPod.