It still could be an issue with your CPU. The athlon's are not as good as the phenom's when it comes to gaming due to the extra cache that is on the Phenoms.
My current Phenom is also a 2.8ghz cpu. Whether or not I overclock it, I can still get around 40 fps on GTA IV with some pretty good settings.
I would say upgrading to the Phenom you listed should help in many respects. But, GTA IV will STILL crawl at times just because of how it was ported. I'm still surprised that the 5770 didn't help though. Strange.
So, in your case, you might be just fine. They saw with the lower speed Athlons and Phenoms, there's not much difference. But when you get to the higher speed chips, the scaling between the two makes the Phenom the better choice.
Shadows is a detail that WILL decrease frame rates. There's nothing you can do about that. With it dropping 20 fps, I'm not sure. Usually you can also determine how detailed your shadows are.
Again, have you updated to the latest video drivers for your card?
In the case of GTA IV, turning on shadows will definitely affect it especially in the city. Consider all the buildings, people, cars that are there, especially the buildings and dropping that much at medium to high is not that abnormal.
Have you considered overclocking your video card and possibly your CPU? When I overclocked my 5750, I gained about 5 to 7 fps. My CPU OC gained me another 5 fps I believe.