That dialog points to the Microsoft Visual C++ 2005 Redistributable as the problem. This is included in Tableau setup, but you might try installing it separately.
Go to http://www.microsoft.com/download/en/details.aspx?id=14431 and install the vcredist_x86.exe linked from there. Then try installing Tableau again.
Just to close the loop on this, in case anyone else has the same problems I did. I tried to install the C++ 2005 Redistributable from the link you gave and got a different error. It turn out that the Windows Module Installer service was screwed up on the machine, and that I had to add a registry entry for HKLM\Software\Microsoft\Windows\CurrentVersion\Component Based Servicing\Version. Once it was added, I could run "sfc /scannow", which fixed .Net, which let me install updates (like 2005 C++), and which finally allowed me to load Tableau. Phew!
Thanks for the feedback,