updater won't update

I've seen this problem in other posts in the Apple Support Community-- but not solved!

The problem is this:

First, I click on "Software Update" in the finder menu. The updater then take a few minutes to determine whether I need any updates.

Once finished checking, the Updater indicates: "New Software is available for your computer." In my case, 12 items need to be installed.

I click "Install 12 Items".

Then a window immediately pops open saying: "To install the updates, you must restart your computer. To finish the installation and restart your computer click Restart". I can also choose "Not Now".

If I choose "Restart", oddly, my computer logs out and takes me to the login screen to enter my password. In other words, it neither restarts, nor does it install anything. Because if I log back in and run the updater, all 12 items are still showing as needing to be updated.

OR,

If I choose "Not Now", the Updater simply closes.Nothing is updated.

In another post, it was recommended to install each of the items one by one on the Apple Update site. This does work; however, I don't really want to have to manually install each update, every time, until this computer eventually dies.

There MUST be a way to fix this.

My computer is an iMac and is currently running Mac OS X, version 10.6.8. I have no other problems with it.