I'm guessing you downloaded the wrong 13.1.
This driver no longer supports pre-5400 cards.
You did not say what version of Windows you're running, try picking your driver under the "Latest AMD Catalyst™ Drivers for Radeon™ HD 4000, HD 3000 and HD 2000 Series" section.
If that doesn't work, you can always try a driver rollback that supports your card.
Catalyst 12.1: http://support.amd.com/us/kbarticles/Pages/AMDCatalystSoftwareSuiteVersion121.aspx
link for xp64 legacy downloads: http://support.amd.com/us/gpudownload/windows/previous/Pages/radeonaiw_xp64.aspx
link for xp32 legacy downloads: http://support.amd.com/us/gpudownload/windows/previous/Pages/radeonaiw_xp.aspx
Honestly, the best suggestion I can give you is to buy a new card. Yes I know, nobody wants to hear that, but an up to date supported card like the 6450 runs about 50$ online, and it probably outperforms your lovely relic. I had to buy one because I had 2 different cards, 1 of which became unsupported by 13.1.
But do try the other drivers first.