Problem starting up and waking from sleep

I have a MacPro 5,1 that is beginning to act strangely and I'm trying to determine if the issues are related.

This has become my start-up routine.

1. Press the power button
2. Repeat multiple times
3. Unplug the power cord
4. Press the power button

I've also noticed that the machine refuses to wake up from sleep. It ignores key presses from wired/wireless keyboards, the mouse, and trackpad. However, the light does stop blinking.The workaround is to unplug the machine.

Since both issues started happening about the same time, I'm wondering if they are related.

I have Applecare so I'm not worried about the cost. I'm just curious as to what the cause might be (and how long repairs might take).

(I cleaned the interior out with canned air without affect.)