Appreciate your willingness to help. In answer to your questions:
1) No. When screen is dormant it is totally black except when I initially press the Space Bar I get - in tiny white letters, for just a moment, in center of screen - "No Signal."
2) Pressing the Space Bar also activates iTunes - if it was playing when I stopped using the keyboard. And Yes, the LED is glowing.
3) Is Mini warm when dormant? Since I've been active all night, I can't tell you right now. Getting ready to do something else for a while and, unless the Reset per BD has fixed something, it should go dormant and I can check the temp.
4) Nudging the Power button does nothing. Have to do complete re-start.
5) Have not tried a restart in Safe Mode. BUt I will tomorrow and report back to you.
THx for your suggestion.
Great news, thanks Sally!
Settings for Energy Saver vary greatly, like it doesn't pay to put the Disks to sleep if say they'll be off for only a couple of hours, but if ambient temperatures are high you may need to sleep them more often.
On my G5 Tower, PPC Mini, & iMac, I never sleep anything but the displays.