Okay. It was the battery! I found an exact replacement GSM battery at BATTERIES PLUS for $159. Great place to do business!
Napa had a replacement relay, which I put in, but I'm not sure I needed it. I'll put the old one back in when I return to Kansas just to see if its good.
Thanks to all for the offers of help and the great advise.
We are no longer "dead in Texas"!
In my best Willie Nelson voice, I'll be "On the road again......."