Right, the SPI pins can only be pulled from the "SPI" header (MOSI digital 75, MISO digital 74, SCLK digital 76). The select lines supported are digital pins 4 and 10. All these are 3.3 volt logic even though there is a 5 volt pin on the SPI header, apparently for legacy. The pinout diagram is at http://arduino.cc/forum/index.php/topic,132130.0.html
SPI "extended" function call documentation for Due is at http://arduino.cc/en/Reference/DueExtendedSPI
It would infer that the pin state is set in SPI.begin as that is when they can no longer be used for general I/O.
Are your pin numbers, select, and function calls all per above? Are your logic lines ok with 3.3 volt signals?