Welcome to this user forum.
Do you have dial tone on your phone?
Is there any noise on your phone calls? Dial 17070 and select option 2, there should be no noise between the announcements.
There is a very faint crackling between announcements??
The line should really be quiet.
Did the number that was read out when you dialled 17070, match your home phone number?
What colour is the light on the BT home hub?
Its unlikely to be the TV, unless it causing a lot of interference to the broadband. This could easily be proven, by turning it off, and seeing if the broadband gets better.
When it was working, what speed were you getting?
I suspect its most likely a problem with the line, which does not show up on a normal BT Line test, so a visit from an Openreach broadband engineer, should resolve the issue, as they have suitable testers, and can check the broadband right back to the equipment in the exchange.
If you could please update this thread after the visit, to confirm whether the problem is resolved.