If a custom keyboard is installed and custom firmware is removed from the console, System Settings will be inaccessible and you will not be able to launch the keyboard. This is obviously detrimental to the overall functioning of your 3DS and should be fixed as soon as possible.

There are other ways to reinstall custom firmware on such a console, but they may require additional hardware. This guide aims to reinstall custom firmware without any additional hardware, but if you have the means, ntrboot will probably be less of a pain.

Unbricking a 3DS with a custom keyboard installed

If you have a copy of any of the following:

Your NAND backup (e.g. 220101_AA000000000_sysnand_000.bin)
essentials.exefs
movable.sed

YOU DO NOT NEED TO MINE YOUR SEED AGAIN.

For instructions on extracting your movable.sed from your NAND backup or from essentials.exefs, see this page.

If Internet access isn't currently set up, you can set up an Internet connection from Safe Mode as the keyboard will still work there (hold L+R+↑+A on boot, then follow its prompts).

Section I: Installing Pokémon Picross

If you can't install Pokémon Picross, there's no point following the rest of this guide and you should choose another method.

Power on your device
Open home menu settings
Scroll down, and select redownload software
Find Pokémon Picross or Steel Diver: Sub Wars
the redownload list
Follow the prompts to download and install Pokémon Picross.

Section II: Mii mining

If you already have your movable.sed, you can skip this section.

Because you can't enter a friend code due to the broken keyboard, you'll need to get your console's encryption key a different way. We can accomplish this by Mii mining.

Follow Mii mining to extract the movable.sed from your console, but do not continue onto the main guide as it suggests. Come back to this page once you have the movable.

Section III: PicHaxx

Now that you have your movable.sed, continue to Homebrew Launcher (PicHaxx).

If everything went well, you should end up with boot9strap installed and the keyboard / System Settings should work again.

Do not uninstall custom firmware again without guidance. You've now seen first-hand how it can go wrong.