I am trying to get Mach 3 to run- everything looks fine on the screen, everything works, but only the z-motor runs and then only down.  The X and y motors don't run at all.  Is it possible that my computer (brand new Windows XP) doesn't have enough power in the parallel port to run the motor controllers?

I am guessing you still havnt configured the ports and pins in mach settings.
Read this http://www.machsupport.com/documentation/