From the MSDE readme file:
If the installation does not succeed, an entry similar to the following will be at the end of the log:

=== Logging stopped: 5/15/03 23:50:34 ===
MSI (c) (6A:CE): Product: Microsoft SQL Server Desktop Engine -- Installation operation failed.

If the installation failed, search for the string "value 3" in the error log. Within 10 lines of the string will be a failure notice for a custom action. The notice will have additional information about the nature of the failure.
I can find 3 "value 3" reerences in the log file, but can't find any decipherable (to me) failure notices\explanations.

I've attached a rar'ed copy of the log file. Would you look through it and tell me if you can determine WHY installation fails?

If I were given to tearing out my hair, at this point, I'd resemble Sinead O'Conner.