Dell Dimension 2350 shuts off, no warnings or error messages

Hi, just about 9pm tonight our other computer started shutting down on it's own and
not coming back on unless you push the power button to do so. There are no error
messages it just shuts off. And the tower is the only thing that loses power. Everything
else running on it continues to have power, like the monitor, the printer, speakers,
ect.

I unchecked everything in mscofig to see if anything was running that was shutting
it off. And it still continued to shut off.

Nothing recently has been installed. It won't stay on long enough to run any diagnostics.
It shuts off even in safemode.

Can anyone advise as to what to do and what might be causing this?

Thanks,

Billie