Mac OS X 10.6.7 freezes on restart

I recently got a Mac running Mac OS X 10.6.7. I installed the software update that was available, and when I tried to restart it, it seemed to be going well until it froze on the original space background.

I tried turning it off and then restarting again, but I was faced with the same problem again.

How might I troubleshoot this further?

I also had the same exact problem with trying to update the software. I have a 2011 MacBook Pro 13 inch laptop running Mac OS X Version 10.6.6. I did a little personal troubleshooting and none of the things listed above seemed to work. I did manage to fix it, however. I did this by starting my Mac up normally, clicking on the Apple logo in the top left corner, clicking on software updates and I let it load to the menu where it gives you the option to install. Instead of installing immediately from there I clicked on the more details tab closer to the left side on the bottom and deselecting the Airport update from everything. After I did that it updated and ran perfectly fine. I am not 100% sure it was the cause but after several hours of troubleshooting and looking up fixes on the internet, that is the only thing I could come up with myself and it seemed to work. I wish you good luck if you have not fixed it yet and if you already have well then I guess i am wasting my time. Anyways, have a good day.