Title states "UNO" but text states "Due".
Do you have anything drawing power through the Due? A display screen? I always need to push restart after power up because the 7" screen i use draws a lot of power. I've measured 600 mA through the whole Due/Shield/Screen assembly. On power the screen illuminates then on reset the sketch runs and the screen template layout appears.
I am currently protoyping a arduino Uno with a 3.5" display screen and am having the same issue of it won't boot up. I need to push the reset pin to get it to reboot and run the commands. How did you go about fixing your issue? Separate power source with separate voltage regulator? for the display screen