Upgrading an old computer!

No, a 3400+ wouldn't be much different than a 3000+.
It's actually a tiny bit faster in 3dmark
http://www23.tomshardware.com/cpu.html?modelx=33&model1=260&model2=262&chart=60
In a few things it's slightly faster, and in other things it's slightly slower. It's the same price as the 3000+, but it includes a heatsink/fan, so it's a better deal IMO.

About the AMD Sempron 3400+, would its fan be able to keep a 6600GT under control?

Ok guys never mind I don't need your help anymore since I asked my parents if we don't upgrade our PC now, can we get a more expensive and better PC later on?They said yes so wohoo!You guys think I should just wait?

I'm not sure what you mean, the cpu fan has nothing to do with your video card.

It depends on if you can wait or want it right now. If you can wait, you will get a better computer, so it may be wise.

Ok well forget the video card....I wanted to say power supply but that wouldn't make sense either so yeah....I guess I can wait.....I'll still come to this website though