Try powering on without the battery in, only using the power brick. It could be that is the issue also. You need to rule out a few things. 1. bad power brick 2. bad battery 3. lose power connection on the laptop 4. the power button idea 5. motherboard.
Quite a few things can cause a PC not to turn on.
Battery is OK.Power Brick also How do you check the others? Thanks for the help