Keep following Einmimirias advice here, but since the launcher is just a fancy Internet Explorer screen, have you attempted to clear the Temporary Internet Files in Internet Explorer yet? (I'm going out on a limb here assuming you aren't using the Mac client)
It solves a surprisingly large amount of launcher issues. This holds true even if you yourself don't use Internet Explorer as your primary web browser.

Heh, last time I mentioned this, it worked, but the main issue was trying to convince the poor fellow that Windows 10 does indeed come with IE, even if it's just a bit hidden lol. Good times that one was.
(Secretly mentioning this to avoid having to explain that to someone new)