Try a reset. If that doesn't work, i would open the ipod following this guide and check all the connectors and make sure they're properly seated. If none of the above remedy your situation then I would look into replacing the display.
We have a chance to guarantee our right to repair electronic
equipment—like smartphones, computers, and even farm equipment. This is a once-in-a-generation
chance to protect local repair jobs—the corner mom-and-pop repair shops that
keep getting squeezed out by manufacturers.
Join the cause and tell your state representative to support Right to Repair. Tell them you believe repair should be fair, affordable, and accessible. Stand up for your right to repair!