From the BIOS screen and POST to counting the memory to loading the operating system, where does it stop? That would be one idea.
Another though if you want some more help is to state what are system specs, e.g. what motherboard is it, what CPU, what memory, etc. since otherwise we are giving very general guidelines here.
A friend of mine gave me a Desktop PC that just stopped working. (Doesn't Boot up) Since I like to tinker with PC's I'd like to know how do I determine where the problem lies? I know the powersupply is OK. Therefore is it the Motherboard or the CPU?. Please let me know how to troubleshoot the failure.