That would leave the CPU, which I have a sneaking suspicion might be the culprit

What makes me say that is you are not getting any BIOS beeps. If it were the memory, you should at least get the memory error beeps. If it is the video, it should still get far enough into the post cyle to beep.
Actually nihil, I was semi corrected by someone... Some motherboards (or most modern mobo's) will notify you of a faulty cpu. But I have encountered mobo's that will not notify you... So it depends on the bios...

I'm leaning toward a construction error on your part somewhere... A good test to see if you had all the case wiring correct (power switch, power LED, speaker, etc) would have been to pull out the ram to see if you get the continuous beeping...

All in all, I admit I jumped on the 12v rail issue instead of keeping an open mind... ...

It doesn't matter now, but you sure you had all the case/speaker wireing correct? Did you check your motherboard documentation? It's bugging the hell out of me ...