If your computer refuses to turn on, troubleshooting the issue can be a systematic process that often begins with checking the basics. 

Firstly, ensure that your computer is properly connected to a functional power source and that the power button isn't stuck. Disconnect all external devices and peripherals to eliminate the possibility of a conflicting hardware component. Attempt a power reset by unplugging the computer (if it's a desktop) or removing the battery (for laptops) and then plugging it back in. Pay attention to any indicator lights on your computer, as they can offer insights into the problem.

Additionally, some computers have built-in hardware diagnostics tools that can identify hardware issues. Running these diagnostics might help pinpoint the problem. If you're comfortable, open the computer's case (for desktops) and reseat components like RAM modules, graphics cards, and storage drives. Loose connections can sometimes be the culprit. Check for any loose cables, especially the power and data cables inside the computer.

Listening for beep codes during startup can also provide clues about hardware issues, so consult your motherboard manual or the manufacturer's website for information on interpreting these codes. If possible, test the computer with a different power supply unit (PSU) to rule out a faulty power supply.

However, if none of these steps resolve the issue, it's advisable to seek professional assistance or contact the computer manufacturer's support. Complex hardware problems may require expert diagnosis and repair to get your computer back up and running. Remember to prioritize safety and caution when working with computer components to avoid causing further damage.