Well, it came to the point where I decided either the motherboard was broken, or I was. As it turns out, this time, it was me.

My problem didn't have anything to do with which drives were on which IDE channel. Instead, I discovered it had to do with jumper settings. The WD's standard jumper settings are Slave, Master w/Slave, or Single. Well I had it set as Master w/Slave. On the old Dell motherboard, it didn't seem to matter, even though the drive was alone on the channel. On the Asus motherboard, apparently, it matters. When I removed the jumper (no jumper sets it as Single), it quickly detected the drive and continued right along booting.

So I was broken, but I'm better now. Thanks for your thoughts, though, Tony.