I'd recommend doing the archive and install from your OS 10.4 disks then... you'd put it in and hold the c key down to boot from the disk...
When the Installer appears, follow the onscreen instructions to install Mac OS X until you get to the screen that asks you to select a volume to install to.
Select your hard disk, then click Options.
In the resulting dialog, select Archive and Install.
Select the volume that already has Mac OS X installed on it (unless you've done any partitioning you'll just have the one volume).
Select "Preserve Users and Network Settings" to keep all network data and Home directory settings, then click OK.
Click Continue to start the installation.
Once the Installer finishes the installation and you've restarted your computer, you may need to reconfigure a few things. Look in the Previous Systems folder that was created during the Archive and Install process, and compare it to your current System folder. If anything is missing, you can move the files over. If any applications don't work as expected after doing an Archive and Install, you may need to reinstall them (I've seen a few apps that need to be reinstalled after an archive and install... particularly font management utilities).
One question... since you still don't know the cause of the problem (and it would be nice to figure it out so it doesn't inadvertently happen again)... did you (or anyone else) add or remove any fonts from any of the fonts folders on your machine?