Did you do the Reset (restart) as described in this document?
http://support.apple.com/kb/HT1320
If the battery is low, you should do this while it is connected to power.
If the screen does not come ON at all, the iPod is probably not getting any power when connected. There are three possibilies. (1) Problem with USB port being used. (2) Problem with USB docking cable. (3) Problem on iPod.
You should do some tests to rule out (1) and (2). And if you can rule out (1) and (2), the cause is likely to be (3). In this case, it may be a bad dock connector on the iPod, or a faulty logic board.