Mac Book Permissions issue

Hi there - on my black mac book I am running OSX 10.6.8.

I have installed Onyx software to help keeping it clean and for general maintenence.
On first run this gave me the warning that the permissions were incorrect and that the hard disc could not be verified.

I then checked this using the Disc Utility application and the same message was evident.
I have attached a screenshot of this message.

Please can anyone advise me as to whet this problem is and how I can remedy it.

I do not have the OSX installation disc as it was bought second hand.

Is this something I could maybe do myself?

Any help would be greatly appreciated!!!!!

The Snow Leopard DVD is only $29.99 from Apple on line. You need that disk to do any kind of trouble shooting and for FSCK repair. My advice is to order it as soon as you can.