Do the following steps and see if it helps.
First, run it only on battery for 10 minutes and see if it is discharging normally.
If it is, switch of everything and unplug the charger from the laptop.
Take the battery out.
Plug the charger to the laptop and the power supply and switch your laptop on.
If it switches on, your laptop is OK.
If it switches on, again turn it off, unplug, put the battery back and give it around 10 minutes charge and then switch it on. If it works normally for sometime and charges normally, your problem is solved.