Can’t type password to reinstall macOS

Reset Both: SMC and the NVRAM, and then give it another go.

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In the SMC link, scroll down to: “How to reset the SMC on Mac notebooks”. Retina Display or Not, being the model and year you provided, this appears to be a non-removable battery. So, use those steps provided for.

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In the NVRAM link, note if you have a startup sound or it. Then press the keys provided.

• Apple Authorized Service Provider (AASP): Rather than using Apple, locate an Apple Authorized Service Provider and see where you can go from there. They are authorized, and are trained in technology. So, use the link in the previous sentence, locate an AASP, and contact them.

• Bootable Installer for macOS Do you have access to another device with Mojave or High Sierra on it? Use that and in the mean time... Go Here: How to Create a Bootable Installer for macOS. It would install all of this using a USB adapter. However, I do not know if it would be a work around to this error of not being able to log in with your credentials. I lost power for weeks a few winters back, and one of these Bootable Installers saved the day.

• Wiping the Hard Drive... If replacing the hard drive comes down to the only option, then have Apple or an AASP replace the hard drive, see if they can transfer data for you from drive-to-drive, and request that the hard drive that is currently in there be wiped clean.

-- TheLittles

Lastly.

Apple Support

iPhone Screensharing

Do you use an iPhone? Calling Apple (as you mentioned in the OP), did you enable the camera on your iPhone while troubleshooting all of this? Enabling it, you can share the iPhone’s screen with them while using the Camera as video.

Enabling it, would let them see it firsthand what’s going on, as and while you troubleshoot. Perhaps they can run you through it better.

Using Two Keys (Command and Spacebar) to “Click” a Command Button

If the “Tab” key works, are you are able to highlight a command button (i.e. “Continue”) with it?

If so, highlight the command button you wish to use and then use it by holding down the “Command” key and then pressing “Spacebar” key to select a command button, as if you were to click it.

Then, proceed from there as necessary.

You do not say what exact Mac /model /year /size /retina /touchbar is this ?

or

what exact macOS you are currently running?

Use the “Tab” key, “Enter” Key” and “Arrow” keys to navigate your way through all of this.

Give Apple staff feedback on this, that way they can know about bugs and Mia-haps.

Go Here: Feedback - Itunes - Apple

Select: iTunes Store

Interesting. If I understand, you are able to get into Recovery Mode, and you are able to use the Keyboard. Correct?

If the mouse does not work, but the keyboard does, then I would think the “Tab” must be not working.