I got it figured out. Someone updated Java to the latest and greatest, and Internet Explorer was updated to 11 as well. After booting into safe mode, changing all vmware related services to manual, then rebooting to normal mode, reverting IE 11 to 10, and reverting Java to the original version it installed with, we are okay. I also changed the service state of the SSO service from Delayed to Automatic, and changed the vCenter server service to Automatic (delayed), from automatic.
Everything seems be working correctly after all of that! 