Q: My ipod nano will not turn on after disconnected from power.  It will however, turn on when connected to power.

That's usually a good indication that your iPod battery's is shot and in need of a replacement.  If you'd like, Apple can swap out the battery for a flat fee.

http://support.apple.com/kb/index?page=servicefaq&geo=United_States&product=ipod

Otherwise, you can also send it to a third party repair service center that could do the same job for a little less. Google "ipod battery replacement" for different options.

B-rock