I'm having a similiar issue, I had a Radeon 3650 and it ran Skyrim fine on low settings, but I just got a Radeon 4650 and after installing, Skyrim suggests high graphics setting but the game crashes within 5-10 seconds of loading now. The one time it crashed to the desktop there was a message on the system tray that the display driver had stopped responding but recovered. I've uninstalled the old drivers, installed the new ones and updated to make sure they were current and tried lowering the graphics to medium with the same result.
A Radeon HD 4650 was comparatively weak sauce when brand new compared to either the HD 3650 (not really that much better) or the HD 4670, compared to which, I'd kinda been thinking it was practically an entry level card ( I was exaggerating the difference in my mind ), but now, three years after its release, that's all it does amount to any more, and you'll need your own thread to discuss this, since AFAIK, this one is still an active thread belonging to the original author.
http://www.gpureview.com/show_cards.php?card1=580&card2=554
http://www.gpureview.com/show_cards.php?card1=580&card2=579