A situation I had once with a cell phone battery
I had a cell phone once that had a bad battery, and it caused my cell phone to go bonkers. sometimes it would shut itself off on a full charge. a lot of the problems went away when I changed the battery... 5-6 years later.
I can think of several possibilities.
- the lithium-ion battery is toast. batteries are cheap. get a new one. or operate without it. it just places a load on the power supply. the charging circuit will recover as soon as a new battery is put in that isn't dead. :-)
- the charging circuit "blew a head gasket"/fried/smoked and you need to replace the motherboard (costs as much or more than as replacing the whole laptop - one person said $800)
- you overreached your laptop screen and cracked your laptop power connector. many laptop power connectors are positioned just behind the screen. if you push the screen back too far, you risk damaging the whole assembly and/or the motherboard.
by the way, nobody uses NiCd batteries in laptops anymore. that went out in the 80's.
li-ion batteries lose their ability to charge over time, especially faster when there's heat (Li-Ion batteries like it cold and so do computers). see wikipedia article on Li-Ion batteries.
sometimes NiMH batteries are used as an older laptop CMOS battery. those can lose their ability to charge with repeated charging, and last about 800-1000 chargings.
no battery likes being left on the charger.