I have been having a ton of fun playing Fallout 4 lately [again, building up my Settlements too much and ignoring the Main Storyline!] and ran into a 'small-but-game-stopping' issue where the TAB key appeared to stop working. "Hitting TAB wasn't bringing up the Pip-Boy anymore..??"
After doing some Troubleshooting and paying attention to what I was doing and pressing... it turned out to be a very simple issue - the TAB key was 'locked' out because of how I had used it in the Console.. Let me explain briefly: