IMac :: Randomly Shuts Down - Instantly Reboots Itself

I do not have AppleCare on this machine. I've got a 27" iMac that will randomly shut down, be it in the middle of playing music on iTunes, while I'm typing a document or while the machine is simply in screensaver mode doing nothing. Usually the machine tries to instantly reboot itself. All too often, it cannot be rebooted and I have to let sit for quite sometime before it will even power back on. Lately the problem has gotten worse, almost never reboots by itself.

Finally, in the last few days, it just won't turn back on. Nothing. My biggest concern is that I have an unreleased music album from an instantly recognizable major client on the iMac's hard drive, not due out for many more months and still unannounced. I can't simply take the computer into an Apple store for troubleshooting as those files are worth and could cost me exponentially more than even a new iMac outright ever would.