Yesterday afternoon was very hot and muggy here in California and the
cooling fan in my Dell Dimension 3000 was reved up to maximum. (I leave
the computer on all the time.) When I came in this morning the
computer had turned itself off, the red light on the battery back up
was on and beeping.
All other computers/lights were still on and there had been no power
interruption. Why did the Dell shut down, and why was the battery
backup beeping and turned off?
You query suggest you have Dell Dimension 3000. Dell Dimension 3000 is a desktop PC and does not have a battery backup by itself.
I am assuming the battery backup you are referring to is a UPS (Uninterruptible Power Supply). If this is correct then by your description of the issues, the UPS may be faulty (indicated by the Red light and beeping).
Disconnect the computer's power cord from the UPS and connect it to a wall power outlet to confirm or rule out the UPS as the offending device.