Q: My Ipod 4th gen 20gb can play music but no display

Try doing a Reset (restart) on the iPod

Learn how to reset your iPod - Apple Support

Do you see the initial Apple logo?  If you do not, it's probably a hardware problem.  If you see the Apple logo, it may be a software (or data corruption) problem.  You can do a Restore on the iPod using iTunes.  This erases the iPod, reinstalls its software, and sets it to default settings.

Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings - Apple Support

After the Restore, if the problem is not resolved, the cause is likely to be a hardware problem.