Try a different cable.
Try powering down the linux machine. I have had problems with the hardware on the PC side before where it has be completely powered off (unplug power cable from back of power supply or switch if you have it.)
Try both the Programming port and the native port independently.
What else do you have connected to the Due? Try adding power to the 12V barrel jack.
Make sure you're reset switch is still switching and isn't being held in the wrong position.
Also make sure all the USB 3.0 vs 2.0 stuff isn't an issue (i.e. stay away from 3.0