Common issue, moving the mouse/pressing keys will interrupt the power button. Basically the power button isn't being held down, but is pressing itself rapidly.
Disconnect the keyboard and battery, then plug in the charger. The MacBook should boot into the OS. If it is not turning itself off, you know the problem is with the power button (attached to the keyboard), so the keyboard will need to be replaced.
Trackpad has cracked since the battery expanded, pushed on the back of the trackpad and cracked it. Replacing this is easy enough.