This is a puzzler. Contrary to your reasoning, though, I would think that since the Fuze will play the demo songs, the hardware is working. So it’s a software question. There is something about your files that is bothering the Fuze. But…what?
It wouldn’t hurt to reload the firmware, even though you are up to date. Get the firmware from here:
http://forums.sandisk.com/t5/Fuze/Sansa-Fuze-Firmware-Update-01-02-31-amp-02-03-33/td-p/139175
Don’t install the updater. Just get the All Regions link for 2.x. Unzip it and drag FuzeA.bin onto the Sansa Fuze driveletter.
And more questions:
What program are you using to rip the songs?
How are you transferring the songs–which USB Mode (Settings/System Settings/USB Mode), MSC or MTP? The demo songs are sent by MTP, but MTP is usually more problematical.