Skydrive missing SysTray icon and can’t fully uninstall/reinstall

I no longer have a functional SkyDrive on my laptop. This is on a Windows 8 laptop, but on my other laptop, Surface RT and Windows Phone, it still works fine.

I have tried to uninstall and reinstall, but the process seems incomplete. In addition, I don't have a system tray icon that I can access to perform advanced functions.

I have uninstalled and reinstalled a few times now. Whenever I do that, it seems to successfully run both ways, but I never get the Sys Tray icon back (and I have also checked Hidden). In addition, both the desktop client (and File Explorer view), as well as the Skydrive Tile, open up to empty folder. They also never show the sync status in the icon, just the cloud icon directly.