Howdy. Sorry you're having troubles. I suspect the charger way more than the battery.
Perhaps a shorted battery could do this, very rare for one to short really. The Solo should try to charge whatever is there, the fact it doesn't show battery level is troubling.
My guess is the charger is collapsing when the load of actually trying to charge the battery happens so the Solo backs off, the charger recovers some and around we go.
I know this is probably a dumb question, but any chance you can borrow or otherwise try another charger or PA (since your unit is old enough for that)?
Batteries don't tend to flat out die like that, the generally get weaker and weaker.
Good luck.
OF
I finally got around to trying another charger, problem solved.
Thanks to you and Q for the assistance.
2 days prior to this situation, I bought and Ascent, and while it does the job, I personally find the Solo far superior, in every way.......