I don't know if you have solved this but if not the way I would approach it is to first of all positively id the "master socket" i.e. the 1st point of entry of the BT line.
To do this I would disconnect all pairs from every socket in the house. Then use a test phone with croc clips (a cheap one off ebay will do) and test each pair in turn until you find one that gives dial tone. You can them be sure you have the "master" socket.
Reconnect just the working pair you have identified with the test phone and try your fillter and router plugged in there.
Just bear in mind that, technically you aren't allowed to touch the back of that socket. So don't tell BT what you are doing/have done. This is the only way you can id the BT pair comming into the property. Unless you can find where it enters the property and follow it through to the first socket.
If you test at this point and it works you know the problem is in the premesis wiring and BT would charge to sort it for you.
If it doesn't then it's likely to be a BT fault and they should fix it free of charge and fit the latest NT5 at that point at the same time.
That's the way I would approach this kind of problem.