The PSU is a 500W Antec Earthwatts. A few years ago, I checked the power load (at the wall outlet) with a meter, and saw about 120W. This was with 4 HDs - exact same hardware I have now, with the exception of the one new HD.
The PSU, and every other component besides the extra storage disks, was bought new, at the same time in may 2008, so it's all about three years old. Also FYI, this thing has been running nearly continuously since I bought it. I do take care to keep it in open space (not in a cabinet like some people) and I remove dust from fans and vents every few months.
I tried running the computer with 4 of the 5 HDs disconnected (from both power and signal) (the new one was one of the 4), and with the 2 case fans disconnected. The only other significant components I have to disconnect are an optical drive, memory card reader (I can't imagine either of those use much power when not in use?), and graphics card. I don't think I'm going to be taking the graphics card out without some reason to believe it's causing the noise.
It does seem like some kind of heat or power warning, except for two things:
1) It started literally immediately after connecting the new HD (at the time when I first connected the new HD, only three HDs were connected - one fewer than normal).
2) It does not sound like any motherboard alarm I have ever heard before - if you don't focus on it, it almost sounds like the whir of a fan (though I am 99% certain it is not a fan), because of how low the pitch is. In my experience, a motherboard alarm is high-pitched enough that when it turns on, you are certain you are hearing an alarm. My roommate can't even distinguish the noise from the fan whir.
I did switch around some of the SATA ports when I was moving HDs around - there isn't any reason this should cause a problem, is there?
Thanks for your help.