Unable to type password and mouse key is not disabled

Tried this yet???

To quickly turn Mouse Keys on or off using the Accessibility Shortcuts panel, press Option-Command-F5 (or if your Mac or Magic Keyboard has Touch ID, quickly press Touch ID three times).

You can also use keyboard shortcuts, assistive switches, or facial expressions to perform mouse actions, such as left, right, or double clicks. Choose Apple menu 

A USB Keyboard.

Another possibility, press the option key 5 times. I don't know if that will work before logging in however.

Can you get hold of a cheap SB KB to try?

You may have to contact Apple support.

Official Apple Support

+1

I wonder if those work before you are logged in.

Sorry... USB Keyboard.

Like this...

Staples Wired Keyboard, Black (51433) | Staples

Win key = Mac CMD key

alt key = Mac Option ket'