The first thing to try is to unplug the main power for about three
minutes or so and try again, just in case it's a 'lock up'.
The first thing to check is the power supply, try a known good one so
that we can eliminate this.
You don't say how old the computer is, if three or four years old then
I would suspect the bios back up battery, sometimes rebooting the bios
by taking the battery out for about three minutes is another option.
But do remember* Removing the battery will result in you having to go
through the bios settings to re-set.
Your first goal is getting the bios to boot, passing that POST (Power
On Self Test) when you power up, the bios checks itself out and if OK
gives a single beep, then hands control,over to the CPU and the hard
drive starts to load data into RAM.
You'll get bios beep or POST as correctly known just with the bare
essentials and that is just the CPU, RAM and Graphic card installed the
rest can be unplugged and that includes the hard drive, this is all that
is required to get the bios booting and if so wish you'll be able to
access the bios set up screen.
So, we're looking at the remaining items, Graphic card, CPU and Mobo.
Just supposing we ran the mobo in the 'bare essential mode' and all was
OK and working you would get something like 'Please insert the disc with
the operating system on' or simply 'NO hard drive' or something to this
effect, it wouldn't just sit there dumb.
Look out for bad caps, their tops should be nice n' flat, here's some
pictures -: 'Don Davidson Computer / Bad Capacitors in System Boards'
) and no gunge leaking