Computer is dead
Most of the time it's power supply failure.
1.A lot of computer owners fail to clean the inside of their computer, plus the power supply out, on a regular basis. I find this occurrence at my shop quite a lot.
Unplugging the computer from power, observing anti-static guidelines, and using a can of compressed air for computers would have prevented this.
Power supply's have a fan for cooling, as well as heatsink's inside. When these components collect dirt, dust, hair, and other foreign objects, the cooling capacity drops tremendously.
Heat = Wasted Energy
The power supply struggles to keep up with the demand of power needed, and eventually components inside it fail.
2.Most power supply's installed in a pre-built computer, are of a low grade of quality. (MOST. Generally pre-built computers manufactured in the last two years, have upgraded the quality of their power supply's, but not all of them)
Saves the computer manufacturer money. These power supply's have low quality components. Gauge of wire used is smaller than it should be, Electrolytic Capacitors are of an inferior grade, transformers are cheaply made, and the rectifier bridge is cheaply constructed, are a few examples.
3.Computers that are built by the owner, and are not pre-built, may have a cheap, or underrated power supply installed. You really have to check out reviews for power supply's on the internet, to see what quality it has. However there are some websites, that 'pump up' the review to stay in good standing with the power supply manufacturer. Generally, if the power supply price is cheap, so is the quality.
There are two other things to look at.
It may be the Power On switch that is behind the Power On button. These can go out.
It could be the motherboard. Most of the time it is Electrolytic Capacitors that are the 'weakest link'. Specifically the one's that surround the processor. These 'Caps' are Voltage Regulators for the processor. If even One is bad, the processor will not work.
No processor, No computer.
How to know if it's the power supply? Use a known, good, and compatible power supply for a test. [Compatible being that the power supply has the required power cables for the motherboard, and enough Wattage]
How to know if there are bad Electrolytic Capacitors on the motherboard?
This website has information, plus photos of bad capacitors,
on Sep 14, 2009