The time is now. I have an electric scooter, and I have some questions about charging issues. See details, please?

I bought a second hand scooter because I really needed one, and brand new is just way beyond my grasp.
It turned out the batteries would not hold a charge long, with a full charge. I could not use it, because it would leave me stranded.
I keep it in my driveway. I had a cover on it most of the time, but winds keep ripping it away. My street is like a wind tunnel, right to my yard. So, try as I might, I have to keep putting the cover back on after big wind storms.
So now my question. If those batteries are dead beyond hope, and they likely are, would the charging indicator still come on, even if they aren’t charging? The light is not coming on when I plug it in.
There is an adapter which goes from extension cord to scooter. If the light does not come on, does that mean it could be something else, or that it is something else?
It was outside through sub zero temperatures, but the batteries were weak when I bought it, so I’m expecting nothing from them at this point. I have no way to take it somewhere, except by riding it, so having someone take a look is no option. I can’t afford a hundred dollars an hour for a house call.