The problem will most likely be witht the GPU unseated properly after the drop. This will need to profssionally be reballed back on the board or replaced.
It seems that you might have a short on some output devices like the mousepad that is causing the motherboard not to function normally for its own safety. I would take it to a well known local repair shop with good reputation and have them test it.
You can hold the power botton for 10 seconds and that should turn the laptop off. Or if you have easy access to the battery would be better to remove it and try to power on the laptop using only the charger.