When you turn it on, can you tell if it's actually trying to boot up? Is there evidence of hard drive activity either from an LED or audibly? How about all fans including the one in the PS. Do they come on? If not, it could be a power supply problem. If you're sure all power is there, you might want to try reseating cables, PCBs etc.
Recently I booted my computer and the monitor would not display. I cleaned the entire unit. I hooked the PC to a different monitor, and still nothing. I replaced the video card and still nothing. I replaced the CMOS battery and still nothing. The light on the motherboard is green, I am sure that all the cables and components works correctly. I am unable to use the monitor, keyboard, mouse, and speakers connected to the monitor. What could be the problem? Is there a simple or any solution that does not involve buying a new computer?