IPOD NANO. The screen lights up but there is no

your screen is broken. the ipod still works in full, so the only problem is the screen.
the back-light still works, this is why the screen is lighting up.

this is problem a hardware, rather than software issue (e.g. physical damage) so its not something that can be fixed with a iPod 'restore'.

you have some choices at this point:

1) try and fix it yourself. this can be difficult but alot cheaper (if your good with directions, pick this)
go to ifixit.com
they have both the parts for the repair, as well as the instructions on how to do the repair itself.

2) send it off to apple to fix
this will be very expensive and slow, i don't recommend this.

3) sell it, and buy a new iPod.