Changing the password doesn't require you to log in. You boot the computer from the Recovery HD. If you can't do that, then you need to start over. If you are unable to do this, then arrange for a replacement.
How to Create a New Admin User Account
Reboot the computer. At or before the chime, press and hold down the COMMAND-S keys to start into Single-user Mode. You will boot to a black screen with scrolling white text, release the keys and wait until it finishes. Enter the following lines at the command prompt pressing RETURN after each:
mount -uw /
^ ^ Note spaces
rm /var/db/.applesetupdone
^ Note space
reboot
After you reboot the computer you will be taken to the Setup Assistant. When you get to the point where you are asked to set up your new user account, create a new admin account. Be sure to name this user account something different than any other account that already exists on the system. When you finish the Setup Assistant, it will automatically log you into the new account.
You need do nothing more. Log into the Admin account only when you need to, such as installing or upgrading software. Log into the Standard account for your normal computer uses. If you prefer using just one account, the admin account, then you will need to make some changes as discussed below.
You can transfer your files from the old account to the new one. See Transferring files from one User Account to another. Once you have moved all your files into your new account, you can delete the old account using Accounts or Users & Groups preferences.
