I never had this problem, primarily because I do not have a iMac, however, a friend of mine had this problem and because it was quite difficult to solve so I thought to help. So these are some answers to the question: why won't iMac start?
How many of you, regardless of the product concerned, look over the instruction manual? No matter how serious or not the problems are, none of us do not even think to do that! Admit it! I do not think you opened the instruction manual to any product. The only contact we have with it is when we remove the product out of the box. So, my first advice would be to consult the manual, you will be surprised how useful can it be!

Secondly, try searching the problem on Google, there are plenty of forums that talk about it. Looking on the internet the problem of my friend, I came across this site: http://www.macfixit.com/staticpages/index.php?page=20031209121115375 that I think will be more helpful. On Google you can find several such sites, in my opinion, very useful.
My friend had a battery problem, nothing serious but the fact that information found on the Internet have saved some money means something, right? I mean I do not think anyone likes to throw some money gully. Instead of paying experts in these things, he just bought a battery and replaces the old himself. So follow my advice and you will get out of these thing cheaper.