Yes, well, what the error is saying is that it can't find the LaunchServices application inside the path you see there.
You can confirm that it actually exists by browsing to "/System/Library/Frameworks/ApplicationServices.framework/Frameworks/LaunchServices.framework" and looking for LaunchServices -- if this does not exist, then you've worse problems. This is a critical system process that should not have been moved or changed aside from system updates, so... it should be there.
As you say you've attempted most of the basics -- repair permissions until no more errors are found, etc -- I'll assume you tried to "Repair Disk" from your 10.4 installer DVD, as well, and have performed the hardware test, as well.
My thought worked in the following way -- your OS version is being reported by the CrashReporter log as 10.4.7, and your Software Update version appears to be out of sync. I could be mistaken here, but my iMac G3 (10.4.7) reports 2.0.5 as the latest version, as does my MacBook (10.4.8). Bypassing Software Update to install the 10.4.8 update may give you more robust error messages, or may actually bring everything up to sync.
One road or another, there're more than a few things amiss.