Taking the liberty of rephrasing your question....
Do you mean "What are the causes (or reasons) for a computer system not to boot"?
No power to PSU.
No power or just some power from the PSU (there are three voltages used to power various components).
If PSU is properly putting out all voltages then the problem could be a loose power connector inside the case and power is not getting to that component. Worst case situation is components such as memory that get their power via the motherboard's circuits.
Most systems provide some sort of error information via beep codes applicable to the motherboard in use. Newer systems provide diagnostic LED's.
Can you explain more about what is or is not happening?
Include full system...