So, it turned out the problem with my Treo was a data corruption problem that commonly occurs during a hot sync. Something about the process causes computer data to go berserk, and then the Treo freezes up. So the problem that began on September 9th probably could have been cleared up THAT DAY if the person I had reached at VZW tech support had diagnosed the problem correctly. Scarily enough, it was PURE LUCK that the smart tech support dude I spoke to on Tuesday, after my new battery did nothing to get the reconstituted Treo working, was someone who knew what he was doing.
George, you deserve a promotion.