Well I meant like a Compaq Model: ???? or something similar so we could see what your working with.
a 1.8ghz Northwood
So it could be a number of things as already stated.
You could buy a power supply tester like this
https://www.amazon.com/Insten-24-pin-Power-Supply-Tester/dp/B005CTCD6S
to see if the power supply failed, useful item to have around.
You can jump the pins on the motherboard to see if it will start, be sure you can replace the wires afterwards, its a long shot but switches do go bad.
At that point you get to the motherboard or the CPU itself being bad.
Somewhere on the motherboard is a clear cmos jumper
short that and hit the on button, you can also remove the battery for 30 seconds.
Put the jumper back the system will...