If you measure more than 5 volts between any 5V pin and any Gnd pin, providing you power the board thru the jack with a 7V to 12V DC, then your board has an issue with the voltage regulator, ask a refund to your board reseller.
Some thoughts about the currents/voltages you will find on a DUE:
Voltage regulator used for 3.3v rail limits the current and allows the maximum of 800ma if external power source is being used. If you draw more current the voltage regulators get heated and temporarily switch off the supply until cooled. However if you power due using USB the USB interface limits the current and allows the maximum of 500ma. If you try to draw more current you might damage the USB port or make it temporarily unavailable. In case of digital out pins you are not supposed to draw more than 130ma, I recommend 100ma.
In case the board is connected with a USB cable , either on the programming port or the Native USB port and you connect a battery pack thru the jack, then the board will be powered by the battery pack and the regulator allows the maximum of 800 mA.