My problem: When I first set up my system, I was not aware that I needed to connect the 4-pin CPU power supply, and I started my system without it. Naturally, I had no signal to my monitor, but all of the fans (CPU heat sink and case fan) ran without issue. When I read the troubleshooting thread (here - http://www.tomshardware.com/forum/261145-31-perform-ste...), I realized that I had not connected the 4-pin power supply for the cpu. After doing so, all of my fans stopped turning when I powered on the PC. When I unplug the 4-pin and restart, the fans resume turning.
I have the system speaker powered and have never heard any beeps at any time.
I have tried every permutation imaginable: 2 sticks of RAM, each stick in each slot, no RAM, I've removed the GPU and tried each permutation again, unplugged the optical and hard drives, everything I can think of. Nothing has changed: I can't boot at all, and when I plug the PSU into the 4-pin CPU power supply, the fans stop functioning.
Everything that I've read indicates this is likely a hardware problem with the PSU or motherboard, but I wanted second opinions before I started shelling out more cash for parts. Thanks for your feedback.
As a cautionary tale to anyone who may have had the same problem that I was having just a couple of minutes ago, the 8-pin power supply cable on this psu splits into twin 4-pin cables that each have a "hook" at the top. This "hook" (I apologize for not knowing the proper nomenclature) must be properly aligned with a corresponding divot in the motherboard.
As it turns out, my 4-pin power supply was inverted--it should have been facing down, when it was in fact facing up. I tried turning it 180 degrees, and--voila--the fans started spinning and the BIOS screen appeared.
After eight hours of cursing God and man, I am feeling a bit better. God bless any neophyte who goes through what I just experienced.