First thing I'll say, is make sure it's patched! I installed it on my girlfriends computer and although it started, it was unplayable. Patched it, and it ran fine! Sure it was slow, but it made SUCH a difference.
On my old system it used to slow down as the games wore on, but yep, the patching really, really helped that. Now, it doesn't matter how big, or how long the game is, it's still speedy.
That said, Civ4 is a beast of a game. Make sure your graphics are set accordingly, with things such as "no effects" "single unit graphics" "no unit animation" etc... all tagged. Things like "show enemy movements" may also slow things down too, but I think that's merely a preference.
After all of that, if it's still too slow, I dare say your system might simply be not up to the task. On paper it looks like it should handle it, but you never know. Give those other things a good go (kill the resolution if needed too!) and see how it pans out. Last thing may be a format and clean OS install. I know my puter gets so bogged down with old crap it really needs a fresh start every year or so.
Best of luck.