Had the exact same issue alot of people here have had. Deleted registry files, all EA Desktop files (to include the hidden ones), nothing worked. Found this via quick google search!
If you're on Windows, follow this link from Microsoft. Follow the steps to download their Install/Uninstall troubleshooter. Searches every single byte on your computer with any information related to EA Desktop, and force deletes it to include the EA Desktop Installer file. From there, re-download the EA Desktop Installer, and it should work!
EDIT: My issue started with trying to use the Uninstall option through the Windows Add/Remove Programs function. Whenever I clicked "uninstall" on EA Desktop, nothing happened. Literally. Its like my computer ignored the command. Proceeded to delete all EA Desktop files I could find, didn't work. Deleted all registry files, didn't work. Saw in the forums to search for hidden files, nothing came up. It was as if my computer understood there was nothing EA Desktop related on my computer, but the Installer application for EA Desktop was still able to find something. Ran that program, and everything works perfect now!