RE: the 42 lb silver tower Mac Pro and the dark cylinder Mac Pro.
The power button blinks, often in patterns of three, when there is not enough WORKING RAM memory to start up. This usually occurs because DIMMs have failed, and you are down to too few working modules to start up.
With the power still on, remove the side door and observe which DIMMs have red LEDs lit next to them. These all tested BAD.
On the MacBook Pro (any of over 50 models) the failure is the same, but the problem may be slightly different (such as dislodged modules) and different resolution. Also, there are no LEDs to indicate which modules failed.