When a PC won't boot it can be due to a failed power supply, faulty connections on the mobo, a fault in the bios or on the mobo, the CPU or the memory. Quite a few to choose from.
This can be dealt with by a process of elimination by stripping the machine back to the least number of components that it needs to reach POST and then adding the parts back in to find what caused the problem.
All you need to have connected is the power supply, mobo & CPU and monitor. Disconnect absolutely everything else, hard drives, Ram modules, PCI cards, keyboard & mouse. If it has onboard graphics use that and remove the graphics card. Hit the power button and if you get something up on screen shut down and then fit one memory stick and see if it will reach POST, if not try another memory stick and so on. If one stick gets you to the POST screen then try it in all the different slots to see if a slot is faulty.
If you have got this far then one by one add the components back in and test as you go until you come across the one part that was causing the problem.
If at the start of this process the machine will not start then remove the CMOS battery for about ten minutes, replace it and try again. If still no go you need to either use another known good power supply or test the existing one with a volt meter, voltages should be listed by cable colour on the PSU case. If the power supply is OK then it has to be the mobo or the CPU. You could test the CPU in a compatible known good PC. And you can test the mobo with a compatible know good CPU and see if it will reach post.
