The only reason that HALO doesn't run on winXP or below is because they don't have DX10 or above.
Your configuration should be reasonable, what Graphics chip is it though? (model wise, not just manufacturer)
Just to clarify, Halo will run perfectly fine in Windows XP. It came out for the PC before Windows Vista was even released.
Halo 2 requires Windows Vista or Win 7 because it had programmed to require DX10 even though it only uses DX9. It was Microsoft way of forcing Halo fans to upgrade to Windows Vista if they wanted to play Halo 2 on the PC instead of on the Xbox.