This question is related, but NOT a duplicate: How to install XNA game studio on Visual Studio 2012?
I read the above mentioned post, and have got xna projects openi
The installer for XNA Game Studio 4.0 has some issues on Windows 8. The installation process fails and removes all installation files. The fact is that the main installer extracts the following installers (at c:\Program Files (x86)\Microsoft XNA\XNA Game Studio\v4.0\Setup):
The conflict is with the first one. So if you manually install all others, XNA should work fine. The problem is that after the installation failure this files are automatically deleted. My solution is to halt the installation process (using the task manager) in the moment when an error was detected, this way the installer don't have time to erase the installation files. Once you have the files you can install it without repeating the procees. It worked for me!!!