How to troubleshoot a computer?
In order to troubleshoot a computer that has so many interconnected parts the best approch would be to "divide and conquer"** which means you will divide one complex problem into a number of smaller problems until it's small enough to solve.
Make a list of all the peripheral devices that are connected to your computer
Note where each one is connected and how it's connected
Leave the bare minimum such as the Tower + Screen + Keyboard + Mouse.
At this point you can narrow down the problem to either some of the previously plugged in devices or a more serious problem with the essential components.
Let's say computer begins to power-up and then shuts down or you can hear the fan but nothing else happens. You can take a guess that it's a power supply issue.
Let's say your computer is powering up but then you see some text and all of a sudden it freezes with partial text, in that case it could be a CPU overheating or some kind of problem with RAM.
Let's say you can boot as far as initial operating system boot sequence but all of a sudden computer freezes or you get a black or blue screen with some text, in that case it could be something corrupted with operating system such as windows or max os and the messeges / numbers on a screen could give you a clue on what kind of error it is.
* Divide and conquer algorithm
In computer science, divide and conquer (D&C) is an important algorithm design paradigm based on multi-branched recursion. A divide and conquer algorithm works by recursively breaking down a problem into two or more sub-problems of the same (or related) type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem. More