Installing .NET 3.5 from scratch was the answer. This took two attempts; the first failed because the installer told me that 3.5 was already installed! The only things I could find which suggested 3.x was the XPS Viewer, which appears under .NET Framework 3.0 in the 'Windows Features' part of the programs control panel applet. Anyway, with 3.5 installed, the VC# 2008 installer finally ran to completion and VC# appears to run fine.
Why did this have to take so long and give me so much grief? Why doesn't Vista display the .NET framework in the add/remove programs panel? Googling about this I discover that Microsoft wants us to consider the framework as part of the OS, and not something which can be installed or removed. This seems ridiculous, given that you can download and run the installers for the various frameworks and it can still be important to know which version(s) are installed.
This is another one of those stupid, stupid, unnecessary things which will drive some folk away from Windows and into the arms of Apple (or even the Linux community).