peacenfunk,
I don't know if it helps but I have and still use a 1st generation Mac mini (Power PC) and before, the same thing would occasionally happen to me. I would guess that it is either one of two things.
I have seen some cases where the RAM becomes unseated and you simply have to pop open the case and reseat the RAM. That usually fixes it.
Or secondly, I don't know if this will help you but whenever this happened to me, I would simply unplug everything and then flip the mini over on a clean towel (as not to scratch it) and then pop open the case (not for the faint of heart, opening it up is a pain and getting the case to fit perfectly back together can be tricky, there are many sites that explain the best way to do this) and then using canned air, I would carefully blow out all the vents and clean out all the dust. After making sure that all the dust had been removed, I would put everything carefully back together and then plug it back in and it would always work. My Mac mini is still working, even today.
I wasn't sure why this kept happening to me but I was guessing that the vents would get blocked with dust and cause the mini to overheat. In addition to cleaning it, to help vent it, I also placed my mini on a small homemade stand that would raise it off my desk a little (but not block the small vents on the bottom of the mini). It seemed to help but I still have to take my mini apart and clean it about once every two years or so.
Best of luck,
Mecha