From what CG has told me, that she can get BBC on her new TV, I suspect the problem may be simply that the TV has not been tuned. If you can get one channel, there is little reason that you shouldn't be able to get them all.
This means going into the setup menu and doing an auto digital re-tune.
The only other thing could be that the signal from the aerial is very weak, but I would expect still being able to get several channels. As the downstairs TV is OK, I do not suspect a weak signal. If the signal is weak, you can get signal boosters, we have one as I run 4 TV's from one aerial.
CG, call me and we will sort this without costing you a call out unnecessarily.
The internet is a different issue, let's get the basic TV working first.