Have absolutely no idea how I managed it, but all of a sudden Visual Studio 2003 thought all my projects were Windows Applications. The .csproj files were still fine. When the solution loaded a shed load of errors like
"Load of property 'AllowUnsafeBlocks' failed."
"Load of property 'ApplicationIcon' failed."
"Load of property 'AssemblyKeyContainerName' failed."
and so on appear in the Task List.
I eventually found a solution on a SAP forum (I have never had SAP installed on this, or any other, PC) - re-register the C# project DLL
regsvr32 "C:\Program Files\Microsoft Visual Studio .NET 2003\Vc7\vcpackages\csproj.dll"
regasm "C:\Program Files\Microsoft Visual Studio .NET 2003\Common7\IDE\PublicAssemblies\VSLangProj.dll"