Hm, if it has a core2, it must be fairly recent. It doesn't say what graphics card is on there, though. Might just be an onboard. This will give a little more information:
Start up paintball2 and type the following at the console:
gl_debug 1
vid_restart
condump skitzo_gl
Now exit and go into your paintball2/pball directory. There should be a skitzo_gl.txt file in there. Attach that to your post or copy/paste the contents here.