There's always power on the motherboard somewhere even if the laptop is turned off.
The power button is not a power isolating button. Its function is to signal the intentions of the user e.g. turn on, turn off, wake etc. It's the same with mobile phones.
Think of the device as being in an extremely low power state when it is turned off, rather than it is disconnected from any power. You need to disconnect the battery as soon as it can be accessed before doing any further work in the device
It's strange that there's no display as the laptop has 2 GPUs, integrated Intel (in with CPU) and discrete Nvidia (separate GPU on the motherboard) so I'm wondering if it is starting or booting at all. (not the same thing)
Does the laptop turn on in as much as the fan starts, (starting) and then the drive activity LED flashes on the laptop indicating it is booting into the OS etc?
The Intel GPU should work until the OS is loaded and then depending on your selected preferences it depends which one you have chosen so you should get the Asus splash screen on startup if it passes POST (power on self test) although you won't be able to use an external monitor to see it as you can't connect to an external monitor until the OS is loaded.
If the Intel GPU was affected so would be the CPU so if it doesn't start it may be a power problem on the motherboard