How can I re-install SQL Server without losing any data under a new version of NT I have installed?

A. This is easy to recover from as long as the original SQL files are all still there.

For SQL 6.5 and below - from the binn directory run the following, making sure the case is correct

setup /t RegistryRebuild = On

The setup routine will now run and ask you all the normal questions. Answer these as if you were performing the install again (put in the same paths etc.). It will appear like a normal install but it will run much more quickly and just insert/update all the registry entries/icons etc. that are needed. None of the existing files will be touched. Once finished you should be able to start the SQL Server service again and access your data.

Microsoft made it even easier with SQL 7.0 and introduced the regrebld.exe command - regrebld.exe /? will give you the options as will the documentation.