What happens if you just plug your iPod into your computer? Does the 'Do Not Disconnect' screen appear, and have the lightning bolt symbol in the top right-hand corner (flashing, hopefully)?
When you let your iPod sit idle while connected to your computer, and expect it to charge, do you leave your computer on and running, or do you put it to sleep and/or shut it down? I'm not an avid PC user, but it may help to know.