Problem solved! Scott, who posted and then communicated via email, was a tremendous help and stuck with me through the process.
So to finish this saga, it turned out that the outlet from the house, which was fine when I connected the extension cord and tested it on the rig's TV - went dead after connecting everything up with adapters. We are using power from the shed and now have lights and heat. BIG sigh of relief. Silver lining is that I learned stuff about the battery/converter/electrical system through this forum and youtube and made a new friend in the process. Thanks again, Scott and everyone who responded with valuable advice :)