Q: is my nano 6th gen repairable? I will not turn on or charge, or should I just buy a new one. It is 2 years old.

Depends on what's wrong with it.  Could just need a new battery.  Here is Apple's repair pricing.  Keep in mind that Apple doesn't actually repair iPods, but replaces them with refurbished units of the same capacity and generation.

http://www.apple.com/support/ipod/service/prices/

There are many third party service centers that will charge less to actually repair whatever it is that is no longer working on the iPod.

B-rock