Do the following steps and see if it helps.
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, the battery is the problem part.
If it doesn't switch on, take it to a service center.
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, your problem is solved.