how too remove log in password

As I understand, you restored your Mini from a Time Machine backup intended for another computer, and the password for that computer is not working, is that correct? That was not a good idea and you may encounter other problems even after resetting your password.

Follow the instructions here to reset your password:

http://support.apple.com/kb/HT1274

If for some reason you are unable to do this proceed to the single-user procedure that follows:

Reset 10.5 Leopard & 10.6 Snow Leopard password

1. Power on or restart your Mac.
2. At the chime (or grey screen if your chime is turned off), hold down ⌘ and S on your keyboard to enter single-user mode.
3. This step is optional, but it’s a good idea because it checks the consistency of the hard disk before moving on: at the prompt, type fsck -fy and press Enter/Return. Wait for the checks to complete before going to the next step.
4. Type mount -uw / and press Enter.
5. On one continuous line type launchctl load /System/Library/LaunchDaemons/com.apple.DirectoryServices.plist and press Enter. There is a single space character before and after the word load.
6. Type ls /Users and press Enter. This lists all of the usernames on the computer – helpful if you don’t know or remember what these are.
7. Type dscl . -passwd /Users/username password and replace username with one of the users displayed in the previous step. There is a single space before and after the . (dot) character that follows dscl. Replace password with a new password of your choice. Press Enter.
8. Type reboot and press Enter.

It can't possibly be that bad. Here is something else to consider.

Follow this procedure to create a new, temporary Administrator account from which you can fix your normal one. Please read everything that follows before continuing. If you have only the one computer you should print it for reference.

• Power on or restart your Mac.
• At the chime or grey screen, hold ⌘ and S on your keyboard to enter single-user mode.
• At the localhost:/ root# prompt, type

fsck -fyand press Return.

This is a simple check for file system integrity and is optional. It may take a few minutes to complete. Be patient. If you get concerned that it has stalled press the Return key. When the integrity check completes pressing the Return key will result in the localhost prompt again.

At the localhost:/ root# prompt, type the following exactly as written, one line at a time, each line followed by the return key. There is a single space preceding the first "slash" ( / ) character in each line:

mount -uw /

rm /var/db/.AppleSetupDone

reboot

The Mac will restart, and then take you through the entire setup and registration process that you have not seen since you originally unboxed it. Do not be concerned - all of your pre-existing user accounts are still available.

Do not elect to transfer your information from another Mac: When you get to the "Do You Already Own a Mac" screen, select "Do not transfer my information" and press Continue. Have your existing Apple ID and password ready. Remember the password you select.

When it completes, log in under that new account. Depending on your OS X version it may log you in automatically. Use System Preferences > Accounts (or Users & Groups) to change your previous account back to Admin, and log out.

Log in using your old account. Delete the throwaway account you just created.

... formated it again for the third time but i am not getting all my disc formated the disc is 500gb but it is saying after formating there is 465 gb and 4 files on it how is this.

That's the first time you mentioned anything about formatting the disk. It seems as though it is damaged, and requires replacement. That would explain your original difficulty. Replace the hard disk before attempting to reload any software.