Mac mini turns itself on

For years, at 7AM, my Mac mini has turned itself on without activating the screen. It is on about a minute then goes back to sleep. Annoying but I've gotten used to it. Yesterday the screen was activated and telling me that the computer didn't recognize the startup disc. Powered it down and turned it back on and all seemed well except that the computer was very slow to respond to any mouse or keyboard input. Then it went into a reboot all by itself. After that things were fine. This morning when I woke it up, it told me an error had occured and it had had to reboot. I sent the error to Apple. I don't have Any scheduled-wake settings set. Has anyone else experienced this? I am afraid that one of these mornings it will be unresponsive and that is not good.