There are a couple of possibilities - it could be that your screen is damaged - which may require a replacement.
The alternative is that this may simply be a software problem - which might be resolved through a hard reset. This will revert your system to factory settings, so make sure you've backed EVERYTHING up before doing a hard reset.
Even if your screen isn't working, you should still be able to back up via your PC (assuming you can still connect your Palm to your PC).
click here for instructions if you're not sure how to do a hard reset or back up your system.