Hello, my Mac Pro had the same symptoms, except that in mine the fan could be heard if you put your ear too close.
I thought it was the graphics card why it didn't give video and turned on, but I took it to an Apple Premium Reseller for a diagnosis and he told me that the CPU Riser Card had to be changed.
I think it must have overheated the CPU because the fan had started to fail me some time before I had unexpected reboots.
Before stopping giving video I had unexpected restarts, then it turned on randomly and finally it no longer gave a video signal.