After a lot of googling, I tried all of the solutions suggested on the 'net:
- registering the C++ COM component \Vc7\vcpackages\csproj.dll
- registering all the COM components in \Microsoft Visual Studio .NET 2003\ including all sub directories
- repairing VS.NET
- uninstalling VS.NET, reboot, installing VS.NET, reboot
When the problem was not fixed even after a complete reinstall of VS.NET, I finally tried installing Windows Script 5.6, even if I thought that it seemed like a far shot. And know what; it actually fixed the problem! After several hours of grief, I am now able to create a new Infopath project in VS.NET.