Just posting this here to help anyone with this issue. I figured it out.
If you have an ROG ASUS Motherboard and installed 'ROG Game First III' and your launcher is not appearing, then 'ROG Game First III' is your problem. For whatever reason, 'ROG GameFirst III' prevents the ESO launcher from appearing.
Run 'msconfig' and disable it via the 'Services' tab. You launcher will launch just fine.
Obviously, you will not be able to use this program after disabling it, but if you're like me, you don't use it anyway. Sounds like there are many issues with this software. Anyways, hope this helps someone!