All you do is use the uninstaller and that will see the system restart as part of the process. Once you are back at the desktop you simply double click on the update to see the installer come up again.
You don't have to pull the card out and physically reinstall it back into the slot. If it was seated down fully when first put in you wouldn't have to worry about reseating it. This is strictly software/driver related and will hopefully correct the problems.
Note that you will want to see the Net Framework 1.1 and 2.0 updates go on before running the installer once the current catalyst/drivers are uninstalled. That will prevent any hangs when reinstalling one of the updates since 2.0 is required while 1.1 has to go on first.
Once you have a fresh start video wise and continue to see problems the next step would be looking at the audio drivers. Are you running onboard or an expansion card?