After realizing the problem, I fixed the date settings and restarted. When iCal came back up, it immediately put up an empty alert window and hung, pegging the CPU. I believe it may have been trying to alert me to every event in my calendar since I started keeping it. Force-quitting iCal and restarting it just produced the same scenario over and over again.
After some poking around, I finally found the cure: in your user's Library/Preferences/com.apple.iCal.plist file, there is an entry named lastHearBeatDate (yes, it's Hear not Heart). Its value was a date string that looked like this:
19691231T224444-0800
I corrected it to somewhere near the right time (20050213T224444-0800), saved the edited plist file, and started iCal. Everything has been fine since.

