I have tried quick restore and hard restore, but nothing seems to work.
I don't know what "quick" and "hard" restores are, but if those are not the Restore that you do from the iPod's Summary screen in iTunes, you can try doing a Restore, in case the problem is caused by corruption in its onboard software or settings. This will erase the iPod, reinstall its software, and set it to default settings.
If that does not help, it is mostly likely to be a problem with the battery. Lithium batteries wear out over time, based on the number of charge cycles, although it is odd that the problem coincided with going to the iPod's diagnostics screen. If the iPod is in good shape otherwise, that model is fairly recent and unique in its features, so you may find it worthwhile to replace the battery. This web page says Apple will do it for $59
https://www.apple.com/batteries/replacements.html
There are other online and local repair shops. If you are good a such things, this web site has DYI repair guides.
http://www.ifixit.com/Device/iPod_Nano
NOTE: You can buy an Apple-certified refurbished current (7th) gen iPod nano (16GB) for $99
http://store.apple.com/us/browse/home/specialdeals/ipod