Hi linnyluke,
Welcome to Apple Support Communities.
It sounds like you have an iPod nano that intermittently displays a blank white screen, and restoring the device hasn't resolved the issue. The article linked below provides the possible ways to resolve an issue like that, restoring the the device from Disk mode or setting up service.
iPod nano (6th generation): Hardware troubleshooting
http://support.apple.com/kb/TS3474
Display shows a white screen
- Try putting the iPod into disk mode:
Reset the device (press the Sleep and Volume Down buttons simultaneously until the display turns black—about eight seconds).
When the display turns black, hold down the Volume Down and Volume Up buttons simultaneously until the device enters Disk mode.
- While the device is in disk mode, sync it to iTunes and try to restore.
My issue is still not resolved. What do I do next?
For information on servicing your iPod, go to the iPod Service FAQ.
If your brother has an older iPod nano, the troubleshooting and service suggestion is very similar, as outlined in the article below.
iPod troubleshooting basics and service FAQ
http://support.apple.com/kb/TS1382
I hope this helps.
-Jason