Make sure all your cards and cables are plugged in correctly. Specially you video card.
Take out any non-essential component (CD ROM, PCI cards[except video],…) and try to boot. Also try swapping power cables and connector ribbons.
At this point you need to replace your motherboard and RAM.
CPUs burn very rarely, and if your PCI cards do not overheat they should be OK. Be very carefull to change the RAM and Motherboard as if you try to recycle one, you might burn the new one. It is a risk!
If your motherboard has failed, it is better to buy another motherboard with a new CPU because old motherboards tend to become hard to find & expensive whereas deals on combo CPU/motherboard are cheap.
Check our Data Recovery if you need your files!
At this point it is either your power supply that is failing or your motherboard. The reason why we can disregard the other components at this point is that if any part fails, your motherboard will give you an error message one way or another by either beeping or giving an error code on the screen.
Most likely your Power Supply is damaged. Don’t worry, it is one of the most failure-prone items in PC systems. It is also very easy to replace and does not cost much!
On the bright side, your Motherboard, CPU and RAM should be OK. (It is very rare that the Motherboard gets damaged, specially if you have a good quality motherboard as they have some level of protection).
You need to get a working power supply and try it on your PC. Power Supplies are not servicable.
But if changing the power supply does not repair the problem then you need a new Motherboard.