You will likely get remote assistance requests from the website. Feel free to ignore those. I'm going to type you up instructions now on how to fix this, give me just a few moments.
First you will need to reboot your mac.. Right as it reboots you want to hold down CMD+S . It will ask you for your password, this will be the last password ***** computer successfully authenticated with. It doesn't know your password *****
You will end up at a command promopt, this is MAC's Single User Mode. Unfortunately all of this is non-networked so I can't help you through the steps.
mount -uw /
From there type
launchctl load /System/Library/LaunchDaemons/com.apple.opendirectoryd.plist
These two commands will mount your filesystem in a way that we can write to and start user services.
It should say something like "New password ***** root:"
Type in your new password *****
now type exit a few times until you end up at the login page for your laptop. You should now see the option to login as other user...
The other user is "root" and that newly set password. You will now be in! From there you can go into system settings (under the apple) and configure your user how you want with the proper apple ID.
After you've done that, login as your normal user, and type dsenableroot -d .. That will turn off the root user.
That should get you back going!