Because of the way you phrased your description, I must respond to some things you said:
The Mac Pro 2010 model does not come on automatically when power is applied. It requires a press of the Power-on button on the front of the chassis.
Most debugging for such fundamental problems is done by removing everything that is in a slot, including all drives, the graphics card, and all the RAM. If the fans come on and the power button blinks, that indicates not enough RAM to start up (but processor, Busses, and ROM are working).
The button battery behind the graphics card slot measures a shade over 3 Volts when new, and if it is substantially spent, your Mac will not start up. The battery holder is delicate, try not to break it. If you choose not to remove it, measure with the AC power cord removed (or you are measuring the always-on power supply).