I am having similar issues. after effects 2015.3 stuck on splash screen.
worked fine for a week and a half and suddenly on splash screen it get's stuck, and gives me a crash window. updated my Nvidia to 368.69 10 days ago and it worked fine. tried to update again (there was an update on 14.7 for 368.81) but that did not help. tried to uninstall both updates and still. uninstalled Ae and reset preferences and still. here is what happens:
no firewall. have AVG Antivirus and disabled it and closed the process in task manager and still.
other cc 2015.3 work fine (Premiere, Photoshop)
This post is not applicable to Windows machine.
Branching it as a new discussion.
Have you tried to right click on the exe file and "Run as Administrator"