Do you think it is only a matter of fuse? I have a Dell Inspiron 2650 laptop. 6 months ago I forgot to place the battery in its place and I turned it on. When I noticed the absence of the battery, I turned it off and I placed the battery. After that, the laptop isn't able to recharge the battery but is still able to work on AC or on the battery. Maybe the thing that I placed the battery shortly after turning off the laptop or something else affected the recharge circuit.
So, I guess, my laptop has the same problem as yours.