Check if all the cooling fans in your computer (or the cooling fan in the laptop) are working properly. There is a fan on the CPU, some graphic cards, in the power supply and in the computer case.
The purpose of the cooling fan is to provide a good airflow so that all the componets can work properly.
If a cooling fan is not running at all (especially those on the CPU and the graphic card), then it's possible that your computer is overheating and it doesn't boot (turn on) due to the built-in safety mechanism designed to prevent severe hardware damages.
Check inside the dektop computer case to see if the power supply cables are firmly connected to the motherboard. If you notice a loosely connected cable, plug it back in firmly because without a good electricity flow to the motherboard, your computer won't turn on.
Note: If you don't know how to do that, this useful video might help you:
Maybe one of the external devices connected to your computer has malfunctioned. Remove any CDs, DVDs, USBs and other external devices (such as portable HDDs) that are connected to the computer. Then turn the computer on and check if it starts normally.
If it does, start returning the external USB devices one by one so that you find the faulty one.
Maybe your computer is on, however it doesn't show anything on the screen because the monitor is switched off. Solution: Switch it on! :-)
Also: Check the VGA cable (the cable going into your monitor) if it is misplaced.
Mabye your computer does turn on, but there are issues with your screen/monitor. Check out the Screen is blank solutions.
Maybe the power on/off button has malfunctioned and that is why your computer doesn't turn on. Replacing the power on/off button will fix the issue.
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