There are a number of solutions to this problem. Unfortunately, troubleshooting this is the most difficult and time consuming, since it could be any one (or two or three) things which could be preventing the system from starting. Here's a list to get you started.

As your system appears to be not powering up whatsoever, then, again, pay most of your attention to the motherboard and the power supply.

It is important to remember that parts, more often than not, fail individually. Therefore, once you find a faulty part, you're probably done. However, I strongly advise you to follow all the steps I've put, just to be on the safe side.

Before you start though, keep in mind that opening the case may void your warranty if you purchased a prebuilt system. You should only do this if you're comfortable with the idea of opening your computer and poking around in there. If the idea scares you, don't do it. If you feel like you have no idea what's going on, but want to learn, go ahead, but, again, be aware that you're potentially voiding any warranty that came with the computer as a whole. I also take no responsibility for you trying these steps, sorry but ive got to put a disclaimer here.

1. Make sure everything is plugged in correctly

This is a very common mistake. Usually it is the motherboard or the boot drive. Some motherboards have two connectors: The 24-pin one, and a small 4-pin or 8-pin square one. If your motherboard does not have both of these, it will only have the 24-pin. Make sure that is secured into place. If that's ok, move on to all/the hard drive cable(s): 4-pin molex/sata power and the L shaped data (if sata) 40-pin if Eide. The data ribbon should trace to the motherboard. Also,if Eide, the red side of the ribbon should be on both pins 1 or both pins 40; it cannot be turned around.

A general review of all the wires should be performed. Where do they start and end? Do the connections make sense? Despite what most people think, the inside of a computer is really common sense; everything fits only in one slot/hole.

2. Clear the CMOS
This is often the solution, and it's usually bloody frustrating because it's so bloody simple once you know about it. All you have to do is find out from the motherboard manual where the CMOS jumper is. Make sure the system has no source of power (meaning the power supply is unplugged and the battery is removed). Then, move the CMOS jumper over the pins that clear it. After a few moments, put the jumper back, plug the power and battery back in, and try it.

If it works, job done, congrats, fireworks will light the heavens and so on. If not, carry on down the list.

3. Strip the system down

The first thing you should do is remove the system from the case**, place it on a non-conductive surface, and disconnect all components from the motherboard with these exceptions
CPU (and heatsink/fan)
A single stick of memory
Graphics card (if you have one)
Power supply
Power button

**(You can do this in the case if you wish, but my preference is the one stated. But do check the motherboard first for any shorting on extra/knackered stand-offs)

This means no drives, no peripherals, no extra ports, nothing. This tests two problems at once. They are the possibility of some peripheral preventing the system from powering up and the possibility of the motherboard shorting onto the case somehow (a standoff that should not be there).

To do a quick elimination (only if the system is completely failing to give any power at all), find where the power button connects and short those two pins for a moment with anything conductive that you have on hand. A screwdriver, knife, coin, or anything metal will work. If the system spins up, you need a new power button. (For anyone else reading: If your system was already spinning up, you can skip this step.)
If the system fails to power up outside the case, here are two things you need to do. First, do a visual inspection of all the capacitors on the motherboard. These are the little battery-looking things. What you'll be looking for is any fluid leaking out of the top or bottom, any...err...puss anywhere on them, or if they are bulging out the top or sides.

While you're noseying around for bad capacitors, take a look at the ATX power connector; make sure it doesn't have any scorch marks or look melted. If anything shows any of these characteristics, your motherboard is almost definitely your problem. If they all look ok, test repeatedly, with each stick of memory individually in each slot (this means 8 tests for 2 sticks of ram on a mobo with 4 slots).

If the system eventually powers up, you've found good memory, probably your only problem, and you're more than likely done. Put the stripped-down version back into the case and secure it. If it powers up again, skip to step 9. If not, you need to remove it again and investigate the setup of your motherboard standoffs and make sure nothing is touching the motherboard where it should not be touched. I know you havn't fitted the mobo yourself, but it's still worth a look after stripping it out. After this is done skip to step 9. If it fails to power up with any memory configuration out of the case, it must be either the CPU, the memory, the graphics card, the motherboard, or the power supply, or any combination thereof.

With the system still out of the case, (or in the case), carry on.

4. Does your CPU work?

There is only one reliable way to test this: Install your CPU into a known good and working system. Use a friend's, a neighbor's, roommate's, or whomever happens to have a system that will take your CPU.
If your CPU allows this known good system to power up, you know that it is good, and it is not the cause of your problems.
If not, you'll need a new one. As above, it's likely that this is your only problem, and once you get it replaced, you'll be good to go.
Note that I did not say to try another (known good and working) motherboard. The reason for this is that there are too many other variables at play: does the RAM work? does the graphics card work? is the power supply working? (I'll get to this later).

5. Does your memory work?
There are two (probably equally reliable) ways to test this, although one is a tad riskier than the other.

The first is to take your memory and pop it into a working test system (maybe the same one you used for the CPU) and, again, see if that system powers up.
If it does, we know the memory is good. For good measure, test all of your sticks in all possible combination, just to be sure that it's not a pair of sticks not playing nicely together.

If the good system fails to power up, you have bad memory and need to replace it.
The other (and riskier) way to test memory is to take known good and working memory and put it into your motherboard. This is riskier because the possibility exists that it is the motherboard that is bad. It is not unheard of for bad motherboards to ruin good sticks of memory. Take this route only if you have no other test system.
If the system powers, you had bad memory. If it does not, the problem is either your motherboard, your graphics, or your power supply.

6. Does your motherboard work?
This is very simple to test: Get another motherboard from somewhere, put together the basic system (as described in step 3), and see if it boots. Windows licensing doesn't come into this.

Again, if the system powers, you had a bad motherboard. If it doesn't, the problem is either your graphics card or your power supply.

7. Does your graphics card work?
This can be tested in two ways, just like the memory: Using the test computer, and a different card. However, this time, the risk of burning a good part on a bad board does not exist, as we have already tried the board. You should know however, that if you are testing a working graphics card with a faulty power supply, and that card plugs directly into the power supply, you may end up with a faulty graphics card.
Something that makes this test easier is onboard video. If your motherboard has it, and it works, but no known good video cards work, you probably have a bad AGP/PCI-E slot. Take a look (and a torch if needs be) in there for bent pins.

8. Does your power supply work?
This is simplest of all; at this point, you've ruled out everything except the psu, so grab a good one and plug it in. Not necessarily the one you've just got but I'd hazard that's going to work.

9. Time to rebuild the system.
Nicely done, all is well. (If you've got to number 9 and it still isn't working, then carry on).

At this point, you have a good CPU, motherboard, memory, video, and power supply. You also have a good case that is not shorting the motherboard. So, the last thing left to test is the rest of the peripherals, if any, and the PCI slots.

To do this, start installing things and/or plugging things in one at a time This way, if there is a bad peripheral (or slot), you will notice it immediately, because all of a sudden your working system won't work after having plugged in that next item. Check the PCI slot for bent pins to make sure it isn't actually a bad card.

This is probably (hopefully) the end of your problem, once you find that bad peripheral or slot. If it's still not working matey, give us a shout back.

Source: Online