Hi Johnny
I had the exact same problem as you. All of a sudden my imac would not boot up, only a black screen appeared. I took it into a dealership, they told me that this was a known problem, and that apple has made adjustments to the parts and that I would have a new part installed.
My imac was only 3 weeks old when this occured. But I am very happy now, it is all fixed, the people at the service depot were awesome. They had it back to me in about two weeks. Its working just like new now.
I'm kind of afraid of problems re surfacing just coz I am totally new to mac in general, and am just getting used to everything...but if anything occurs it is under warranty for the one year plus another 2 with apple care.
My advice is don't worry too much, because this is a known issue, and has occured to quite a few machines, apple is aware of it and will do their best to help you. I know it is scary to see a machine break down like that so fast, but with a little time your machine will be up and running. My logic board was replaced, the guy at the depot told me that if my imac broke a few monthes ago i'd be waiting long time for my part but he said I should be happy it broke when it did because the parts no longer had such a backorder on them.
If you google this issue you will find lots of issues with this. The thing is everytime something wrong happens people post things, but everyone with good experiences dont post, so you may get scared reading people's comments. But just remember all the people who got imacs that didnt break down or have power supply issues probably didnt write much about their experience.
I'm not sure where you live but since you do have a depot in your city you should get your computer back within a few weeks, maybe sooner.
At first i was very scared and didnt know what would happen, but I just got my computer back last week and its been great, I hope you have the same experience as me.
Well take care for now, and hope your imac gets better soon! I'm sure you miss it!