I have a partial DVD image on my hard drive that contains a single video that is composed of multiple VOB files on the DVD.

If I drag any one VOB file into Popcorn, it correctly grabs all the VOB files and stitches them together for benefit of the preview slider in Popcorn.

However, when I export (to iPod, optimized for TV, h.264), Popcorn only exports the first VOB's worth of video and then just sits there doing absolutely nothing but spinning the progress bar.

This appears to be a bug with no workaround since you can't meaningfully drag in multiple VOB files.

I am concerned about your original DVD image. What exactly is a partial DVD image file? If you use a regular DVD image, does it work? How was this partial image created?

For multiple VOB's the process is to select the VIDEO_TS folder in Popcorn rather than drag in a VOB. Otherwise you could use something like MPEG Streamclip to convert the VOB set to MPEG and drag the MPEG to Popcorn.