it sounds like your original stb had a feature called an 'analogue bypass', but your new one does not.
- as you have found, not all customer service associates are aware of the difference.
Allegedly there is an add on, which will restore the feature, but availability may be regional and may not work with all stb models.
If you post the model number of your box, someone with more experience of this than me, may be able to help more.
I should add I am still on an analogue connection - with an aerial combiner, not a bypass - which would be no good for you with your weak signal