IMac turned itself off and won't fully turn back on

Question

My iMac turned itself off this morning; all I was doing was typing, nothing intensive. It wouldn't turn back on.
I first got a wired keyboard and mouse and tried resetting the SMC. No success.
Next I took out and put back in the RAM (and it was unplugged). After repeatedly pressing the power button, I got a single beep out of it. I personally don't think it was high enough of a pitch, but I read that it might've been because the computer didn't read any RAM.
I might've again taken the RAM out, this time also unplugged. After more repeated pressing, the fans came on, but then dead again.
The third time, the fans came on and half of the dong played, but it was cut off.
The forth time the dong fully played, but a second after, it turned off again.
All of these times involved unplugging the computer for a few seconds and then repeatedly pressing the power button; I might've taken the RAM out all of the times too, but I don't remember now.
Two or so weeks ago, I did have a kernal panic while I was editing in iPhoto, and I believe it's the first for my iMac. About a month and a half ago I had a graphics problem where using exposé to show all windows caused the whole screen to become jagged 'shards' of colour (it reminded me of broken pieces of glass). While a restart fixed both of these problems, the graphic problems are not new for this iMac (though I had never had the shard effect before).
Two more little things that I'm unsure if they're related: last night, it turned itself on from sleep, but it does this every other night, so I don't think last night's special; and every time I got it to turn on, I felt that I had to give the power button just a short burst of force, as if holding it for even half a second wouldn't get it to turn on.
Does this sound like the logic board, or less expensively, the power supply? Since it attempts to come on here and there but gets cut off, what does that say with respect to the logic board?
The computer turned one year in August 08, and there's no AppleCare. Even though the warranty's gone, would Apple have any negative view if I opened it up to get my HDD? I can get the screen off with three house suction cups; my HDD was last backed up four days ago, and of course, I had just typed about 3000 words for a story I'm working on between last night and this morning.
And lastly, if I make an appointment with the Apple Store (two hours from here...) and they want to take it in, will they take out my HDD right there and give it to me if I don't take it out? Four days is so tremendous in this situation. I will not part with my HDD.

Answer 1

Perhaps. While I guess they're certified, I still trust Apple the most. Also, if it is a logic board problem, and it is widespread, hopefully this could be free. I don't know how a reseller would handle such a situation. I just want a file off my HDD!
I can confirm that it never really powers on unless it's been unplugged for at least a few seconds. So far, the longer it's been unplugged, the longer it stayed on. There were hours between the times I almost got into my account, and then the login window.
I again switched the MacBook and iMac's RAM, but doing this makes a senseless result. The MB's light simply stays on (no fans or screen, but when I turn it off, I do hear it 'de-whir'), and the iMac just quickly turns on and then off, as it has been after a 5-30 second unplugging session.
I guess this is the rebellion of a Revision A machine.