Thanks a bunch for the detailed response pofdlp!
The Wikipedia link was also helpful.
All right, I'll check my PSU. I'm away from home right now, but I'll check it tomorrow and get back to you on the state of its connections. If it helps any, I know it is a Corsair 750W, so I hope it does have enough juice!
I do have an ATI Radeon 5800 HD 1GB graphics card, so that may be hogging all the power, but again, I won't know for sure until I check it myself. I might also take some pictures of the computer interior and post them for clarification.
You are correct about the WD getting enough power: it does spin up, but one of three things happen:
1.) The drive does not mount; Windows doesn't "see it" at all.
2.) The drive attempts to mount but fails, with the Windows notification area message: "The device has malfunctioned."
3.) The drive does mount, but it appears as unformatted (it's formatted NTFS) and when I try to access its contents from My Computer, Explorer locks up until I either restart it or pull the plug on the drive.
These symptoms lead me to believe that the drive is connected to the card properly, but somehow the signal is lost. I thought it might be because there just isn't enough power for the USB 3.0 hookup. I can attach the drive to my computer's USB 2.0 ports without issue.
Thanks for the Device Manager tip to increase bandwidth; I'll give that a shot tomorrow and post back with my results.