Dead as a doornail

Out of nowhere, my IMac won't start up - no chimes, screen, fans --nothing. An Apple tech said it could be as simple as a dead power cord, but that seems a little too optimistic. I've done the easy things: disconnected, waited ten minutes, reconnected, etc., to no avail. I'd like to try the power cord first but in searching for a compatible one, I'm only seeing ones that work with 2011 or newer. Any thoughts about that?

I suspect it's at least the power supply. Is there a way to test that before I spend a few hundred to purchase/install a new one? I'm on the brink of declaring this DOA and not worth fixing, but I'd love to get another year or two out of it.

Any help is much appreciated.