I suffered through agonizing "freezes" with my new mac and took it to the Apple store three times for this. The cursor would move and the icons in the dock would animate, but I couldn't open anything or do anything with programs already open. At the Apple store the mac behaved so the techie people could not determine a cause. They did tests and permissions fixes and an archive-and-install, and this last time the guy said sorry but it's time for erase and install.
During some of these visits I took out my mouse and used it with the mac, so the guys there knew I had one and used it.
When I got it home again it froze again and I had a thought. I tried the track pad and it worked. It wasn't the computer; it was the wireless mighty mouse. It doesn't always do this, of course. It just loses something sometimes. Could be the bluetooth connection, could be something mechanical. It was able to move the cursor around but clicking didn't work.
So I didn't erase and install. However, I now know how to do that with the minimal amount of fuss. The techie guy was quite helpful. So if I do ever have to go that route I will know how.