Hi, and welcome to Bleeping Computer! The Dell Dimension 3000 does not have an AGP slot, which is what that graphics card uses. It doesn't have PCI express slots either which are the newer slots for graphics cards. So, if you really wanted a graphics card you would just have to get one with PCI interface. They're not really the best graphics cards, but if your not planning to do any intensive gaming or video editing one would probably be fine.
I have a Dimension 3000 also and I just ordered this card
. It seems pretty good, and has pixel shader 3.0. I'm hoping to receive it tomorrow, and I'll post if its good if you are maybe interested.
Oh and if you have any other questions about your dell dimension 3000 system I know quite a bit about mine so maybe I could help you
"I think there is a world market for maybe five computers." - Thomas Watson, Chairman of IBM, 1943