Ran into the same problem as you folks. Same exact "battery lighting up fan coming on battery lighting down(?), fan still on. With 2 different batteries. I figured that it would be incredibly rare for 2 entirely different batteries of 2 different ages (1new,1not new) to have the same exact issue. So i looked towards the drone itself.
Where the battery connects to the drone, on either side of the connection there are an arrangement of 4 pins, set up in a vertically oriented rectangle. It appears that over time the fit into their receptacle has compressed the two pairs of pins (top and bottom).
Using something non-conductive you can come between those pins and spread them ever so gently (once i used a plastic picnic fork, and another time i used my auntie-girlfriends state issued ID card).
Like everything in life, after a little spread, things get much easier, and reliable.