Short story long, yesterday evening I turned the computer off for whatever reason and noticed that the cooler fans were still illuminated. They weren't supposed to be when the computer is turned off. I then unplugged the PSU from the power strip, and when I plugged the cord back in, the RAM chips illuminated but nothing else did. And the computer wasn't even turned on. I was like, "This whole thing is messed up."
I took blackghost's advice, removed and reseated the RAM just for the hell of it, then decided to clear the CMOS. After a reboot, the machine posted! Who knows what truly happened. So thanks to all for your suggestions.