Have you tried to use the key you received from Amazon and applied it to EA's Origin client? Maybe you can download and install using EA's copy instead. If it's a game from EA or uses Steam as DRM, I usually just enter the key into the clients instead of download from Amazon.
Also, I've noticed that Windows 8 is a little weird about installing programs from time to time. Usually if I run into the problem you described, I have to reboot and the problem typically resolves itself (lets me install).