I have a Tivo series 3 and it seems that shows on some channels (like HBO) are protected and thus you can't download to your machine with Tivo Desktop. Is there anyway around this?
They're "protected" for this exact reason. They don't want you to move them to your computer.
You'd have to look into some kind of DRM circumvention, and I'm not going into that.
If you use a non-digital (so, not HDMI) to output the show to a video capture device or card, you should be able to record the show just fine.