Imac turned off randomly than wouldn't turn on?

So I have had this similar problem in the past but it was a failed atempt at trying to turn it on for several days. I ended up bringing it to apple and getting it fixed, good thing I was under waranty or else it would have cost me around $600. So now not under waranty a couple months later you can see why this would concern me. It was working perfectly fine today until randomly it just shut off. I tried turning it on to no avail. I unpluged it and pluged it into another outlet with nothing working. I did this on several outlets until it finnally started to turn on. As I started to breath a fresh breath of air it just shuts down mid boot up. This happend on two occasions. I called it a lost battle and left it alone for 45 min. When I came back and tried to boot it up again it amazingly works! As I am typing this on it now. I am still quite concerned though and am just wondering if anyone can help me out or set me to ease about the situation.