Did some more tests with the DUE and the Grove Base Shield and luminance sensor.
First I used a serial port testing program that sends the users text from the IDE's serial monitor to the DUE and bounces it back to the monitor. If the Base Shield is in place on the DUE this does not work. But if I remove the Shield it does work. This verifies that the PC, the USB-Serial cable, the Arduino IDE, and the DUE itself are probably OK.
Secondly I took the Base Shield off from the DUE, restarted the PC then verified/compiled and uploaded the Luminance sensors demo sketch without errors to the DUE. I then shut off the PC, added the Base Shield to the DUE, and started the PC up again, and the sensor output was printed to the serial monitor OK.
So I may not have a convenient solution, but I definitely have a workaround.
It looks like the problem was the Base Shield. I noted some odd things in the IDE when I was trying to upload to the DUE with the Base Shield. Parts of the IDE menus would blank out like the IDE was confused. Also the IDE would often give an error during uploading attempts that no board was found on the COM port it was listed on in the IDE as well as Windows Device manager.
Any comments on why a Base Shield might cause problems on a DUE appreciated.