Reinstalling doesn't delete the preferences and it's very important in lion and mountain lion to remove the prefs after a major version upgrade, like 10.6 to 10.7 or 10.7 to 10.8.

Go to your username>library>preferences and delete:

com.adobe.PhotoshopElements.plist

Adobe Photoshop Elements 10 paths

Adobe Photoshop Elements 10 settings

and any lockfiles with the same names.

That library is hidden in 10.8. To see it, in the finder click the Go menu and hold down the option key. It will appear below the little house for your user account. While you're in there go to the Saved Application States folder and delete everything for PSE.

It wouldn't hurt to repair permissions, either.

Try creating a new administrative user and running the program there. Does it work?

And did you delete the saved application state and repair permissions?

About the new user or about saved application state + repair permissions?

Did you go into the Saved Application States folder and delete the one for PSE as I suggested in my previous posts? That is crucial. It's in your username>library>Saved Application States.

Do you mean you don't know how to repair permissions? Go to your Applications>Utilities>Disk Utility and click the name of your hard drive in the list on the left. Then click Repair Permissions. It takes a while. Don't get upset about any messages you see scrolling through the window while it's working. All is well unless at the end it throws up a big red warning that the repair failed.

Okay. To create a new user go to system prefs>Users & Groups, click the lock so you can make changes, then click the plus button at the bottom left of the window and create a new account. For the type of account choose Administrator, then log out of your current account and log in as the new user and see if PSE works any better.