Titan Fall Free Game Time won't activate on my account after a friend played on my PC

Your problem may differ.  Game Time isn't available in segments.  It starts running, and doesn't care if you quit, the timer will still be running.  At least, that is my personal understanding.  Instead of digging up this relatively outdated and probably not very relevant thread to use for a "Me, Too", you should choose a more recent and more relevant one, or better yet, start one of your own.