A bad power cable is not a common cause of a PC not turn on but it does happen and is very easy to test for. You can use the one that's powering your monitor as long as it seems to be getting power, one from another computer, or a new one.
1. Replace the CMOS battery, especially if your computer is more than a few years old or has spent a lot of time turned off or with the main battery removed. A bad CMOS battery is a relatively common cause of a computer that looks like it's not receiving power.
2. Make sure the power switch is connected to the motherboard if you're using a desktop. This is not a very common point of failure, but your PC might not be turning on because the power button isn't properly connected to the motherboard.
3. Test your power supply if you're using a desktop PC. At this point in your troubleshooting, at least for your desktop folks, it's very likely that the power supply unit in your computer is no longer working and should be replaced.