One day my Mac Mini would not wake up. Leading up to this it was acting a bit unreliable.
I started with first unplugging the power supply from the logic board and measuring the power supply output with a multi-meter to ensure that was not the issue. It puts out a simple 12V to the logic board so it is easy to check. In my case that was rock solid so I assumed that was not my problem, which took me to the logic board. Checking the power supply only required removing the plastic back and the metal antenna cover plate. This provides enough access to pop out the power supply connector and measure the output voltage.
The Logic Board repair was actually quite easy following the directions on iFixit! There are a lot of screws so keep them sorted in the order you took them out so you can put them back in the order they where removed. I have a silicon mat with pockets all around the mat to help keep them from rolling away and to keep them organized in groups.
Make sure you buy the Logic Board removal tool, your not going to get it removed any other way. You will also need the special heatsink compound they sell if you don't already have some and I used isopropanol alcohol and cotton swabs to clean the original heatsink; they do sell a special cleaner. (You could see where they missed a corner of the original processor when they applied the heatsink compound at the factory and hence probably the reason for the failure.) Less is more when applying the heatsink compound, but a complete coverage is nessesary to ensure heat transfer to the heatsink; it is used to fill all the micro gaps between the processor and heatsink to create 100% contact between the two.