i think to describe that system as crappy is a bit tactless,you dont want to give it away,do you?
anyway,have you got up to date drivers?ati can cause conflicts with their drivers,i belive they have been described as"fussy"
it could be a power supply problem,i would try the drivers first,dont forget to delete your old drivers first in"add and remove programs"first or you will get conflicts when you load up your new drivers.
you could try a test to stress your graphics card,"3d mark 2001 or 2003 for example,you can use these to test your graphics card performance,you can then compare on line to similar spec pc,s
use google for ati drivers and 3d mark tests,