I finally got VS.NET 2003 working. It turns out that the DVD drive on my laptop has a firmware issue that means that an installation from DVD fails randomly.
OK - I copied the entire DVD to hard disk, then installed from the hard disk. Still, the installation was failing.
Next, I ran WinDiff, to compare the files on the DVD with those on the hard disk. Hmm, some checksum mismatches. So, I manually copied the dodgy files from the DVD, until WinDiff reports no differences.
Installation now succeeds! However, although VS.NET 2003 launches, the Splash Screen is blank, i.e. it does not show my name as the licensee nor does it display the icons for the features installed (C#, VB.NET, J# etc.). More worryingly, the IDE disappears from the screen if I invoke various IDE functionality:
1) Click an item on the Start Page
2) Try to debug a C# project that has breakpoints
3) Invoke the Macro Editor
Clutching at straws, I decided to run WinDiff again, this time comparing the Setup files on the hard disk with the runtime copies made by the installation process. Weird - there are some differences in various DLL files, including those that seem connected with the functionality listed above. Anyway, I manually copied all the mismatch files, then relaunched the IDE. All the same problems exist.
Finally, I ran the Repair option in the Setup, then rebooted for good luck. Bingo - this time it works and, so far, all the features I have tried function as expected.
Shame it took 4 weeks of banging my head on a wall to get there.