Why is my Mac Mini turning off automatically?

For some reason, my Mac Mini G4 (1.42) keeps turning off automatically. I've tried to use different power supplies (85w and 110w), applying new thermal paste, booting into a 10.5 install disk, and none of that worked. It would turn on very briefly (30 seconds to a minute or so), then turn off. If it matters, the hard drive was dead inside the computer. However, I've tried turning on the computer w/o a hard drive and still got the same result. Please help and thank you for your time.