Failure to boot can be caused by a number of different things but the bare minimum hardware required is:
Powersupply
Motherboard
CPU with HEatsink & fan
1 stick of RAM
graphics card (onboard or plug-in) with monitor
Keyboard.
Start your troubleshooting by disconnecting /removing all drives, pci cards, extra ram, USB devices, printers etc.
In "barebones mode" will it boot into bios and give a display? Any POST beep?
If no display or beep try booting with ram removed. Any Beep?
replace the ram and remove the graphics card.
try to boot. Any beep?
If the powersupply is shot none of the above tests will work.
To isolate which component is bad you need known good spare components to swap in/out.
Of course your problem could be something as simple as a card or cable slightly out of position. re-seating everything may solve it.
If it boots up in barebones mode then the problem is with one of the peripheral devices such as drives or PCI cards.
reconnect them one at a time with a bootup attempt between each reconnection.
If after testing you are still unable to isolate the problem you might have to take it to a tech. the other alternative is to start buying replacement parts such as powersupply, motherboard, cpu in the hope of getting it right before you run out of money.
I used to have a signature but it disappeared and I just couldn't be bothered writing another so please feel free to ingore this.