You're correct about the manual stating that the engine must be running. I always ran mine ( I don't think they would have worked otherwise ) and was frequently plugged in.
Here's a link to that manual for others to see.
http://support.powergearus.com/techdocs/82-L0368.pdf
I have posted PG's email address many times on this forum. They may have saved you a lot of frustration and money. Once again , they're address is
info@powergearus.com .
They respond very quickly and have called a lot of members here ( they will call if necessary ) to walk them through a few error modes .
I would shoot them an email if I were you and see what they have to say about what happened to you. Please update us if you do.