The most common way that a computer "won't turn on" is when the PC actually does power on but doesn't display anything on the monitor. You see lights on the computer case, but nothing shows on your screen.

How To Fix It

1. Monitor Is Defective/Loose VGA Cable Connection. Try to swap monitors with another computer to check if the monitor is defective or not. You can also try to reinsert the VGA cable to the VGA port of your video card to see if the connection is loose or maybe the VGA cable of you monitor is defective.

2.Test your monitor to make sure it is working properly before you begin troubleshooting.

3. Make sure your computer has completely reset - make sure that it's coming on from a completely powered-off state.

4. Troubleshoot the cause of the beep code if you're lucky enough to get one. A beep code will give you idea of where to look for the cause of your computer turning off.

Return here and continue with the steps below if you don't resolve the problem by troubleshooting to the specific beep code.
5. Verify that your pc power supply voltage switch is set correctly. There's a possibility that your PC wouldn't power on at all if this switch is wrong but an incorrect power supply voltage might also prevent your computer from starting properly in this way too.

6. Clear the BIOS memory on your motherboard. It will return the BIOS settings to their factory default levels. But if clearing the BIOS does fix your problem, make sure any changes you make in BIOS are completed one at a time so if the problem returns, you'll know which change caused your issue.

7. Reseat everything inside your PC. Reseating will reestablish the various connections inside your pc.
Reseating the following and then see if your computer begins to display something on screen:

Reseat all internal data and power cables
Reseat the memory modules
Reseat any expansion cards

Above all, you can reseat the CPU only if you suspect that it might have come loose or might not have been installed properly.

Read more: http://trendymediablog.com/2014/10/how-to-fix-a-computer-that-turns-on-but-displays-nothing/

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