|Do you ever see anything at all on the screen?|
If it turns out to be a hardware fault then working down to component level is virtually a thing of the past. No circuit details are available or individual parts. Complete boards or units have to be changed. Clicking sounds could be a sign of hard disk failure.
I know it's a strange thing to ask but does it "sound" as if it is starting up - sometimes you get to recognise the noise sequence if you have had a computer for some time.
Always pop back and let us know the outcome - thanks