I came up against this same problem myself. I tried everything in the Microsoft Workarounds with MSConfig, flatcopy, only installing 1 component, etc. and nothing worked.
Finally, I hit on this idea: I took a computer that MSOffice installed on without the office1.cab error and put my CD in that computer. I then shared that computer's CD-ROM drive on my home network and installed Office on the destination computer over the network from the CD-ROM drive of the computer where I knew it worked.
Result, the error was bypassed and Office installed correctly. You just have to find a computer where it installs okay. I used the CD-ROM of my laptop to install office on my Tower. Hopefully this will work for you too. I suspect the problem will appear again when adding additional components, so I would suggest a full install.
I have done this for a few people and it has worked 100% of the time.