I ran into the same problem. The solution is to uninstall "Microsoft Visual C++ Compilers 2010 Standard - enu - x86", but there's no entry in Control Panel/Programs and Features to do this. Additionally, you may need to uninstall:
Microsoft Visual C++ Compilers 2010 Standard - enu - x64
Note: that there are 2 spaces between the words C++ and Compilers.
The way I figured it out was to by doing a registry search for the above 2 terms. When you find a regkey with a DisplayName that corresponds to each of the above strings, look for the value in LocalPackage - you'll find the name of the MSI file to use to uninstall using the instructions below.
Launch an command prompt with administrative privileges. Navigate to C:\Windows\Installers. Execute the following command:
C:\Windows\Installer>msiexec /x <LocalPackage reg string value here>
Answer 'Yes' to the prompts and this will clean up completely. Repeat for the other string if needed. This will allow you to do a full install of Windows SDK 7.1
Note that in my case, I had Visual C++ 2010 Express edition installed followed by VS2010 SP1. Based on web search results, it seems this problem is caused by installation of the SP1. Also, I wanted to uninstall everything and only install Windows SDK 7.1 - so, I wiped stuff. Another alternate solution is to uncheck "Visual C++ Compilers" when installing Windows SDK 7.1 and that will keep the existing newer version and install the rest of the SDK properly.
This page has additional, relevant & important information: http://msdn.microsoft.com/en-us/visualc/gg697159