One potential solution is that the "NOT REG" message might mean I need to change the VGA input mode with the projector's remote. I don't have a remote for it and it costs $30 and doesn't have Prime shipping. If I buy that and it doesn't work, I'll have spent nearly as much trying to get this projector working as I spent on the projector itself.

This part of the manual(page 37) makes me think that the projector's "auto" method may be malfunctioning and that setting the signal type manually with a remote could make it work.