I have a very similar issue; the installer for version "184.108.40.20681" (i.e. the current version at time of writing) fails because it can't find "Evernote.msi". Having read the above I've established that:
"C:\Users\<USER>\AppData\Local\Evernote\Evernote" is empty, and is the only thing in the parent directory.
Downloading the installer for the version I currently have (220.127.116.1125) gives me an error: "Newer version is already installed"
I can't uninstall to start from scratch, using the uninstaller, because it's corrupt and keeps asking for a valid source of "Evernote.msi"
I'd be inclined to manually remove everything and start again, but I don't know what I need to delete? Presumably some settings and registry keys some where? Is that a good path to go down?