Laptop on, black screen, won't power off

First thing to do is connect to an external display, see if the external display lights up.

It's possible that the laptop thinks it's closed, and therefore once higher functions take over it assumes a signal from the inaccessible power button must be erroneous.

Shine a bright flashlight across the display at an acute angle while you inspect it from a normal viewing angle. If you see something that resembles a boot logo, Windows splash screen, Windows Login, or your desktop, your backlight and/or inverter in your LCD has failed, although it wouldn't explain unresponsiveness to the power button.

Most modern laptops (AFAIK) use permanent magnets in the display and magnetic force sensors in the base to detect screen closure, as no moving parts=fewer failures, but they can be faked out by external magnets.

You need to turn it off.

Remove the power chord.

Remove the battery.

Let it sit until it turns off.

That should only take a second or two once the battery is removed.

If it is an Apple machine which does not have a removable battery, it could take hours to run out of power.

Once it is off

Put the battery back in.

Plug in to power.

Turn on.

Report back here, tell us what happened.