I can't log in to my user account using my password and when I boot on the recovery mode to change the password,it accept my password to be root, I entered new password I get a message
"Authentication token manipulation error"
"password unchanged"

I don't have a way of testing it with a Mint rescue disk, but I would expect that entering as root

to prompt me to enter a new password for [username], so long as [username] already exits in /etc/passwd.

Could you post the sequence of commands and output here? It might give us a hint.

The sequence of commands and output is as followed;

itstraining-system-Product-Name ~ # passwd itstraining
Enter new UNIX password:
Retype new UNIX password:
passwd: Authentication token manipulation error
passwd: password unchanged
itstraining-System-product-Name ~ # _

Humm... If iT is a fresh install you could just reuse the partition for it and reinstall it.
Otherwise it looks like something is wrong in /etc/shadow(?)(Where The Encrypted Passwords Are Stored) or the hash (the magical thing that encrypts your password).
Are you sure you entered the password the same way both times?
Most people say don't do this as root but: "startx"; this will start the GUI and maybe somthin under manage user accounts will help. If it asks for a password and blank isn't correct try "debian".

Are you sure your hard drive isn't damaged?

Iam connected to the internet but by typing "startx" it says something about

xinit:unable to connect to x server: Network is unreachable
xinit:server error
xinit:error in locking authority file /root/.Xauthority

and the debian think is just not working, is there any other ways?????

That's wired, knowing that x11 doesn't need Internet to run... There is an x server (used to handle the x11 libs for programs) but no x network...
Ohhhhhh!!!!! Linux Mint is a people-friendly distro, never have to log in as root means that no default configuration was ever created (the .Xathority it wad talking about).
Try su itstraining; it should drop you to a prompt as your user, then try startx again; if it doesn't work come back.
If manage user accountsdoesnt work, get all important data off the computer and reinstall it (not using a funky filesystem, stick to ext2 ext3 or ext4) That always works!

When you boot in recovery mode according to this post, The file system is read only by default. This would prevent you from "changing" the password on an account.

1) Switch to root
2) mount -rw -o remount /
3) passwd [username]

Hope that helps.

I did that in Ubuntu yesterday!
How did I forget!
Sorry for all the grief!
$DIETY export Zssfssz="Bad Kitty"

Hay chiefs I tried it all out but it didn't work out
I think I should be reinstalling the destro.
i'll come back to you after reinstalling to say how it goes

however thank for helping!!

Cheers to you'll

Hay I had it worked out after reinstalling the Mint.
Now I can do what I want with the Mint

Thanks again for the advice

Hay hi there, I'm doing python programming in Linux and of course its my first time doing programming and using this python programming tool, and I just want to ask if any of you could give me a website that I could go to for TUTORIALS.

You might start at the python site, link below:

http://www.python.org/about/gettingstarted/