Hi Skylar,
The 5.9's come highly recommended as their my favorite Catalyst drivers for that card (9600 series).
What you should do is download the hefty (41mb) ATI UCI download at:
https://a248.e.akamai.net/f/674/9206/0/www2.ati.com/drivers/9-08_mmc_uci.exe
This is the Unified Components Installer for Windows XP, which includes Windows Media, Media Encoder, MDAC/DAO and several other Microsoft component updates needed for a HW accelerated card like the 9600 series.
You should also try disabling Fast Writes in the BIOS, then also try reducing AGP to 4x for tests to see if this helps, changes or corrects the problem.
If you bought a true-blue, made by ATI full-retail 9600, you are also entitled a single user license to ATI's DVD Decoder and MMC (MultiMedia Center). It will depend on the CD that shipped with your Radeon. If you have a full retail, ATI made board, try the following link (~6mb):
https://a248.e.akamai.net/f/674/9206/0/www2.ati.com/drivers/atiCDwiz.exe
It will ask you to insert your CD to be checked for license, and if present allow you to download and install the ATI DVD decoder. After this, you can install and use ATI's MMC (~32MB):
https://a248.e.akamai.net/f/674/9206/0/www2.ati.com/drivers/9-08_mmc_enu.exe
The first link should fix your problem with Windows Media files and Media Player. If you still have issues, there are also hotfixes and updates for Windows Media Player for HW accelerated and HD files you may need. I'd start with the UCI install and post back if you still have issues.