Most of the sites I checked said you have to use VLC in order for Handbrake to be able to record copy-protected disks, supposedly because HB runs the movie through VLC and records the stream. Maybe the newest version of HB had to conform to DMCA or some Windows update defeats its ability to record copyrighted discs.

I got it to work using the forum post you linked. Downgrade to 0.95, copy the dll file, and run in WinXP SP2 compatibility mode. Not sure if all three are necessary but it works. I might try different compatibility modes to see if it matters. The video quality on normal looks about the same as with the program I used before, PQDVD, which recorded in xVID avi format. The h264 mp4 file is about twice as large though. I'll change the settings for maximum quality to size ratio.

Thanks for all the help!