I was stuck loading on the menu screen too. I had played it for quite a bit already, so it was quite weird that it did that. What I tried is powering off the xbox by pressing and holding the xbox icon/button on the console for 5 seconds. shutting it off that way. then when i turned it back on, I was able to get Fallout 4 to load up properly to the main menu. I didn't have to re-install, but i was close lol
I have this same problem, same thing having played already, got it digitally, and now wnt work, nothing I do is working, deleted and reinstalled and is still doing it
Did you try holding the power button (xbox glowing icon) on the console for 5 or more seconds, while powering down? that did the trick for me once i powered it back up after.