Well, though I had already done all that was suggested by jbraveman, it still didn't work. So I shut the PC down and restarted at least once, maybe twice, and though it had already installed all the software on several previous startups, it kept re-installing it (or adding more, I suppose, though I think it was stuff I'd seen it install before) and suddenly the damn thing started working. Transferred two DATs last night.
However, I can't monitor the audiophile with headphones or analog outs, and can't heard it using the PC's headphone jack since its internal soundcard is disabled. There must be a tweak somewhere in the Audiophile's settings that allows the headphone jack to work, but I can't find it.
Thanks to jbrraveman for the suggestions. It caused me to reexamine all the settings, and that caused me to get pissed and try the multiple restarts, and that did it.
O