OK, one Western Digital 320 GB HD upgrade and 737 MB OS 10.5.7 update later, iCal is still not agreeing to do anything.
Hold on... I just did a Finder search for iCal and found TWO versions lurking in Applications. (?!??) One was 1.5.2, and the other 3.0.7. The one in my dock was the old one... lo and behold, 3.0.7 works just FINE.
ARGH!!! <beats head against desk>
Thanks for the help, everyone. Now I just need to save me from myself.