if there's no life at all or only the power light comes on but nothing else happens, the PSU (Power Supply Unit) inside the computer-case may be faulty. They are not repairable items. You buy and fit a new one, or get someone to do it for you if you are at all unsure about doing it yourself.
Take the opportunity to replace the faulty PSU with a more powerful one (ie higher output wattage). It won't do any harm to any components, but it will mean it's not running at full tilt all the time, so it less likely to fail from overloading.