I was using my computer last night and it was okay. I turned it on today and it won't power on. This one of the most common problems that come in for repair. So as a consumer what can you do yourself. The first thing is to make sure you are getting power to the computer. If you have the computer plugged into a surge protector make sure it's working. Alot of them have warning leds that light up indicating a problem or fault. It may also have a reset button, so make sure it is in the proper position. If it is out try pushing it in to reset it.
The next things I would check is to make sure the power plug is in securely in the back of the computer. If that is okay you can check a few things inside the computer. Slide of the side panel and look inside at the motherboard. One is it full of dust in the cpu fan and heatsink. If it is you can blow it out with canned air or an air compressor. I would suggest holing the fan from spinning with a pencil. Next inspect the motherboard for any bulging capacitors or leaking capacitors. If there are this indicates the system took a power surge and damaged the motherboard and possible other components. If you can replace the motherboard with the same exact motherboard, then you may be all set. Remember to use good esd protection such as a esd wristband grounded properly to a esd mat that is grounded.
The final step would be to test the power supply. You can buy testers that you connect the various power supply connectors to. You can also use a digital multi-meter, but you need to know what you are doing. Another easy test is to use a good know power supply and connect it in place of the one in the case. You can also test the power button with the digital multi-meter. One other test is to remove the power button connector on the terminal block on the motherboard. The use a small flat blade screwdriver to momentarily short the power button pins.
If you have done all these you could take it to a repair service center. If the computer is 5 years or older, then it's time to replace the computer and transfer data if needed. You could also take it to a service center for further repair.