For the sake of rigour, we need to be sure that your power / Start button is not defective. It is not very likely that this is the case, but in case it is you better find it out now before replacing every part on your PC, and it only takes 2 minutes. If you are sure that it is not your Start button that is malfunctioning, you can proceed to the next step.
Warning: If you don't feel confident opening your PC then refrain from touching anything and call a technician.
We are going to manually bypass the Start button and see if it does the trick.
You need to get your motherboard user manual and look for the motherboard layout. Look for the part that connects to your Start button as shown below by the PWR symbol.
All you need to do is connect the lower part of the PWR column to the Reset column. This will turn your reset switch into your Start Switch.