As it turns out, the user had deleted the McAfee Anti-virus program directory. No mean feat in itself. Which in turn led to the error message above when the user logged on.
So I knew McAfee was probably the cause.
When McAfee AV installs, it replaces the registry entry for vbscript.dll with scriptsn.dll. When the user deleted the Mcfee directory, it deleted scriptsn.dll, which is why it couldn’t find the script engine.
The solution in this case, was to re-install Windows. Deleting the McAfee directory will cause other problems. Less desperate solutions can be found in these articles: