|The term CPU is often mis-used.|
The computer case that most of your computer components are in IS NOT A CPU !
The CPU - Central Processing Unit = microprocessor = Processor, is the large integrated chip on the motherboard that is usually removable and installed in a large socket - the CPU has a large heat sink ontop of it and usually a large fan ontop of the heat sink.
There is usually nothing wrong with the CPU a.k.a. Processor itself.
99.9% of the time, the Bios DOES NOT spontaneously get corrupted. There is probably nothing wrong with it.
It is extremely unlikely there is anything wrong with the power switch.
However, sometimes the case button that presses on it can get stuck inwards such that the power switch is always depressed - make sure that button is not stuck inwards.
Since you tried, I assume, briefly, shorting the pins for the power switch and the computer did not fully boot, it's extremely likely something else is wrong and there's nothing wrong with your power switch.
If you always have video while booting the computer BEFORE Windows is supposed to load, but you have NO video after that, that problem is usually easy to fix, and there's probably nothing wrong with your computer.
If you get no video at all.....
If you have not changed which ram you have installed in the motherboard since it last worked properly, the most likely causes of your problems are the ram has a poor connection in it's slots, or your power supply is failing.
See response 2 in this - try cleaning the contacts on the ram modules, and making sure the modules are properly seated:
For a laptop, or netbook, you must remove both its main battery and AC adapter before you do that.
For a brand name computer, see the Owner's or User's manual if you need to - how to remove or replace the ram is usually in that - it may already be in your installed programs. If you can't get into Windows, it may be on a disk that came with the computer, or you can go online and look at it or download it - it's in the downloads for your specific model.
For a generic desktop computer, see the mboard manual if you need to - how to remove or replace the ram is usually in that.
Failing power supplies are common and can cause your symptoms.
Check your PS.
They often partially work, fans and hard drives may spin, leds may come on, yet you may get no video and the mboard will not boot all the way.
See response 4 in this:
If you can borrow a power supply from another working computer, try connecting that.
If it is failing, you can usually replace it with any decent quality standard sized standard ATX PS with the same capacity or greater.
Standard (PS/2) power supply size - 86mm high, 150mm wide, 140mm deep, or 3 3/8" h x 5 7/8" w x 5 1/2" d , or very close to that, though the depth can be more or less for some PSs.
Don't buy an el-cheapo (in quality)PS.
See response 3 in this: