I don’t think there’s much hope.
Refurbs are always a gamble–SanDisk doesn’t fix them, so you are at the mercy of the seller, whoever that might be. SanDisk doesn’t guarantee them.
You could try reinstalling or updating the firmware.
http://forums.sandisk.com/t5/Sansa-Fuze/Sansa-Fuze-Firmware-Update-01-02-31-amp-02-03-33/td-p/139175
But if it’s a hardware problem–as I suspect it is, like a broken backlight–it’s time to look for another player.
The Clip+ apparently uses the same processor as the Fuze, though it puts out less power. You can add a microSD card to the 2GB of this one: