I noticed the same thing. Apparently Logitech would prefer you buy a new keyboard rather than buy a new battery!
I tried similar things with TWO of these keyboards that had not been used in a long time. It wasn’t until I stumbled across this website that I even realized there were batteries in these. Duh. Anyway, after numerous attempts to recharge the solar panels using various bright lights, I concluded that the batteries were dead/dying in both units. Reordered…will see if I can get them going with new batteries when they arrive.