It is requesting 4 passwords?? WOW!!

Hard to see how you would get through an installation without being asked for a password......

Boot from your install disk, and do ctrl-alt-F1 to get a terminal. Mount the partition where Mandrake is installed, and then find the passwords file in /etc. Then edit the entry for root---removing the first "x" that appears between 2 colons. Reboot and all should be fine---when you first login (as root), you will not be asked for a password. Then do "passwd" and enter your new password at the prompt.

If you cannot do this from your install disk, then use a "liveCD" distro such as Knoppix.

By the way, is it Mandrake or Mandriva? (The latter is more current)

its mandrake 10.1
i don't have live cd linux, like knoppix
then what to do
if i reinstall then will the problem persist, or it'll go off
need urgent & possible solution

What do you mean by 'as soon as mandrake starts' ? As your a rookie (according to your own words):
1)
Your system boots and shows you some POST info (amount of memory etc).
2)
Next it will start booting and you will/might see the bootloader (grub or lilo, not sure which one). In case of a multi boot, this will allow you to select the operating system
3)
Next the operating system will be loaded. Once Mandrake is loaded, you will either have a graphical screen or a text screen where you can login.

In which of these steps does it ask you for a password? I assume the last one.
In that case, which username did you use? There will always be a user root (and you might have left that password blank during install; not sure if that's possible but it's definitely not advisable).

// edit
As a moderator moved a post in this thread, the rest of this post did not make sense anymore.

Did you try to boot from the install disk to edit the password file as I suggested?

If you re-install, then it **should** ask you for a root password, and a username and password.

Getting a Knoppix live CD is a good idea--no matter what else happens. get it here: http://www.knoppix.net/

I have lost my root password, so I tried to boot using edubuntu live cd in order to mount my ubuntu server installation partition in order to change root password,

but I couldn't get root credintial cause I don't know root password.

can anybody tell me what is the default password for edubuntu live cd?

Any live cd I have used has either NO root password, or simply uses the password "root". I have not used Edubuntu.
Have you checked their website?

I would also always keep a Knoppix CD handy...

Thanks pixellany you are always on the front line..

I solve this problem by using sudo, before when I use sudo without any argument the system ask me for (I think) root password which I don't know, this time I used sudo with an argument and surprisingly got root prompt

now I will try to change the root password and after that correct grub configuration which the original problem I have.

Ubuntus (Kubuntu, Ubuntu, Xubuntu, probably Edubuntu too) have this policy: by default the root account is locked (i.e. it's password is set to unknown). The first user created during setup is granted access to sudo command, the following users created don't get this right by default. The first user created during setup may then, if it's needed, "unlock" the root account using "sudo passwd root" to set the root password.

Sudo asks always for the user's own password, never root password.

EDIT: and if I'm right, the LiveCD default user has access to sudo.

what did you said here was exactly what I experience with my system, but couldn't change root password, I will try to use what you said : #sudo passwd root

I think I am using the wrong command

it was very interesting to play with linux system

I loved it after working long time with Windows.