A few questions...
Was a different version of Office previously installed?
Does the crash occur regardless what component is opened (Word, Excel, Access...)?
The log file is good, but what is the original exact error message and when exactly does it occur?
What OS?
Is the install being deployed over a network or installed on each workstation using a CD?
Do a search for that DLL (efxlgs.dll), right click it and select properties. Does that give any clue as to what it is associated with?
Try renaming it to 'efxlgsTEST.dll' and see if that resolves the issue.
A tool that may help is DLL Show (http://tinyurl.com/eagpj). You can download a trial version to see if that helps in tracking down the purpose of that DLL.
something to try... If a previous version of Office was installed, pick a workstation, uninstall Office from Add/Remove Programs, un-install ALL instances of Office and Office products there, manually delete the Office folder in Program Files, reboot and then reinstall Office 2003.
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