you got it wrong if you don't use the laptop battery and want to save it then
You store it in refrigerator charged to 60-70% of capacity, using it once in 6 month to check.
In this manner you can store for many years loosing very little capacity about 2% per year
but once it's dead it's dead and freezer wont help,
Unless its new battery and got discharged to 0% sometimes you can jump start it
(but im not confertable telling how, bit dangerous)
Won't hold a charge, or won't charge at all when plugged in to the wall? If the latter, it is most likely a bad power jack. Common issue with laptops. Good computer shops can replace the power jack inside the laptop.