What's Compatible with my Computer? Help please.

What is your PSU? If it is not higher than 300W/350W the best choices are the ATI HD 5670 or GT 240. Even if you had a 1000W PSU your CPU would bottleneck your system.

Your motherboard does not support any dual core CPUs, so you should consider a new PC (build it by yourself, of course, because the PCs in stores are more expensive and weaker than the ones you build) IF you want a better CPU. If not, just buy the 5670 or 240 and you'll be fine  

Your motherboard is pci-e 1.0, therefore any newer card will only run at the most, half of its throughput.

The only place you could find a dual core processor for that mobo is on ebay or a store that sells used stuff.

You could get s775 motherboard and a dual core cpu for less than $100 though.
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

The dual core wolfdale celeron would be 3x as fast as the cpu you have now and it's highly overclockable and much more efficient and runs cooler.
Easily 3.0ghz on stock fan, 3.5 or more with aftermarket fan.
If your on an extreme budget, this is the way to go, however, keep in mind that s775 has long been obsolete as well.

I would suggest if you can afford it, looking at putting together a newer system.

Sorry to be rude, but any modern card will be held back by your Pent.4 cpu.
Really, buying new card for this old machine is wasting money, you'll better save your money to BUILD a whole new system.
I'm sorry, but that's a fact.