My take about it is: you've got to decide if it's worth the effort.

Your unit is currently under a widespread recall from Apple, because in certain situations the battery would swell and/or lose fluids, causing several disruptions in the operations of the iPod Nano, from extreme heat to inability to hold a charge, passing from a damaged logic board.

So, I'd read here and check with your local AASP, and/or with the website if you're eligibile for the still available repair program.

If not, and/or if you don't want to through the simple apple replacement program, you can find a new LCD here, along with a guide. It's going to be a timeconsuming job, but doable.

Check this question for references: it can be as simple as dismantling your unit and cleaning the connector, or you're going to need a new LCD.

Of course, if you choose the repair path you won't be anymore eligible for the AASP replacement (Apple will check for water damage and mechanical damage/opening of the casing), and viceversa.

Thus I say, especially if your symptom goes along with other malfunctions as listed in the Apple Support Page, check for the replacement program. If you're willing to take on the risk, sure your battery and logic are fine, get a new LCD.