Try downloading '3DMark05', google it and run it, if its a graphics or temperature related problem then its sure to die whilst running that.
Also, click start and in the 'run' box type 'eventvwr' and have a look in there for any errors at the time of the crash then google what you find.
To be honest, i doubt very much if the graphics card itself was knackered, as they arent the kind of things that will die slowly....they either die or work. I would say its a driver or temp issue.
Try updating your graphics drivers, chipset drivers and sound drivers and see if that helps.