I got back from the Radio Shack with a new solder iron ($ 8) and combination spunge/iron holder, also ($ 8) .

I've never done a solder before, but I stripped down the iBook, let the iron heat up, and prodded the loose pins on the problem IC. I'm not sure how good the reflow was, but I'm typing this reply on the iBook right now, running 1 hour, 30 minutes without a restart. For a 6-years-old machine, this is still a really competent laptop.

Thanks for the help, everyone!