Fedora 7 Installation Guide
Unfortunaly, the previous ATI driver (8.37.6), nor the current ATI driver (8.38.6), or even the hotfix (8.38.7) are compatible with the X server in the FC7 distribution.
As pointed out at Phoronix.com, the latest release (8.38.6) has very little changes and completely ignored Fedora 7 users who have waited over a month for a functional driver.
"The AMD 8.38.6 display driver had introduced Red Hat Enterprise Linux 5 packaging support along with fixing a few bugs, but the driver was one of the least interesting releases in recent times." http://www.phoronix.com/scan.php?page=article&item=764&num=1
Given that this release focuses on packaging support, ATI are still prioritising cosmetic changes over functional aspects. Whilst packages are a 'nice to have', basic functionality is far more critical.
However there exists a workaround. You can get the driver working by installing an older version of the X server which is compatible with the current ATI driver and then compiling the driver. The disadvantages are obvious: No updates for the X server, bugs and security holes of the old X version remain unfixed. Further you could break package dependencies and block updates of other packages. Although there's a step by step howto you could get into serious trouble if you do not understand what you are doing.