I have dell 'DHS' model
old post. PC is 16 years old today, (junk and not worth $10 used)
1: run it on line power only main battery out. now.
runs now,yhes, then the battery was shorted, get new one.
or run on AC only for ever.
2: RTC coin cell is dead, buy a new one and put it in.
no RTC COIN lasted 16 years, not a single one, impossible!!!
so get rid of this old coin cell., buy a new one, spend $2
3: Now the CPU fan works, and stays on, in some BIOS you can check a box say fan is always , on do so and now it only changes speed. if the fan is dead still then it may be bad. this old easy.
4: CPU overheat, I have never seen any CPU to heatsink
thermal compound last for 16 years, (mine does but not yours)
I use very top quality thermal grease (compound, no aging) ask.
5: The Power pack can be bad. (if PC dead with main battery out the pack can in fact be just bad.
6: is the screen 100% black at all times? no text ever?
most PC this old the CCLF back lamps are dead.
that is why most PC this old are worth nothing until year 2010 made. a fact. get a newer PC with LED back lamps.
ask for advice on this, have lots.
My posts can be all wrong ,after all I can not watch your screen
and do simple tests.
but the fan dead is very very serious matter.
I even strip off all modules in the Laptop, to prove there are no shorted modules in the PC. shorts cause power to shut of.
BY DESIGN.