Update your graphics driver. Still, it may not at all suffice. Your computer is simply old...
Update. I replaced the most recent vidoe driver (dated 10/2012) with the latest driver from HP (dated 09/2009). Adobe no longer warns me about an out of date video driver, but still crashes with the same details.
Then I guess a refund is my only option.
Moving this discussion to the Premiere Elements forum.
To look into PrE crashing, or hanging, I would look at this FAQ Entry, which begins with setting up PrE to run properly, then goes into tuning up one's computer and OS, and finishes with troubleshooting tips, with links on doing that troubleshooting, working up in "degree of difficulty:" http://forums.adobe.com/thread/792580?tstart=0
If you are unable to use PrE, Adobe offers a 30-day, money-back guarantee, so just contact Adobe, within 30 days, for your money back.