You may find this article helpful in troubleshooting the iTunes installation issue you are experiencing.
If iTunes has been previously installed, I would recommend completely uninstalling iTunes and all of it's components in the order specified in the article below. Once this is done, attempt a download and install iTunes.
If you receive any errors when uninstalling, follow the steps in the article below. This article will also provide steps for troubleshooting installation issues as it has a helpful link to utilize.