Okay, here's what I know about a digital signal - you either have it or you don't. Analogue you can get a range of quality - from total shite snowy, to clear as a bell can see the nits in the kids hair clarity. So if you don't get a strong enough signal with digital you just don't get anything.
So in this case, what's likely is your signal booster isn't boosting enough. The fact you have to plug into a digital box in one TV would indicate you don't have a strong enough signal without it. May I suggest you take the digital box to the second TV, plug it in there and see if that rectifies the problem?