Well, it was a hardware/driver issue. The first thing I did last night was
to pull the old PCI modem out (since this was the one piece of hardware that
had to search for drivers). When I rebooted without the modem, Vista went
into repair mode (like so many times before) but this time it reported a
conflict with the modem driver and removed it. It then rebooted back up fine!

It's a little scary to me that a single driver (especially one that Vista
installed and reported was working fine) could basically stop the entire PC
from working. Looking back, I don't think SP1 was the issue, especially
since using previous restore points didn't resolve the problem. I think it
must have loaded the modem driver and then started the SP1 installation
shortly after, so the problem didn't appear until SP1 tried to reboot.

I did successfully load SP1 last night, using the network install version.
I'm guessing Windows Update would have been successful as well now, but I had
several replies suggesting the network install so that's what I used.

Thanks to everyone for their help! If you are still in a helpful mood, I'm
just making a new post called "My PC won't stay shut down!" that you could
look at. Thanks again!