I finally got my PowerBook back yesterday. They had hung on to it for two weeks waiting for the new logic board to come in, gave it back to me to use for a bit (although it was more broken then than it had started out), took it again on Monday night, replaced the logic board yesterday and brought it back to me yesterday afternoon. I swear, I had been using it for about an hour when it put itself to sleep again. So it appears as if this whole ordeal was for nothing. Hurrah.
From reading the Apple Support user forums, it would seem that this problem affects a fairly large number of 15 inch PowerBooks purchased at around the same time as mine was. You would think they would issue a recall or something, but so far that hasn't happened. It also seems that people who are having this problem who still have warranty coverage (under the AppleCare agreement - I do, only because work bought my computer) are trying to get their computers fixed and having the same problem. The people doing the fixing don't seem to know how to fix it.