Phone line disconnects when Router plugged in.

I have a three BT telephone lines coming into my house.

Yesterday I found one of the lines didn't work and upon checking I
found that also the phone line with my Broadband service didn't work
but the broadband worked without any apparently problem.

BT came today and found something wrong at the pole at the back of my
garden. I didn't get a chance to talk to the linesman to find out
exactly what was wrong. But checking afterwards I find the phone line
with the broadband attached only works when the Netgear DG834G router
is disconnected but the dialling tone is lost as soon as the router is
plugged in to the BT socket.

I phoned BT again and after much time their Broadband support people
said to replace the filter at the phone socket. I have an old
broadband connection with the ADSL V1.0 filter screwed into the BT
socket. I unscrewed the filter socket and plugged in a different type
and the same thing happens, the phone line only works when the router
is not plugged in to the filter/BT socket. The router works all the
time.

BT provide the phone lines and I use another ISP for the broadband
connection. The original installation was fitted by BT.


My questions are:

Who is responsible for the filter? When I took it off the wiring
inside the BT socket is exposed.
What should I look for to fix this?
Is it likely to be a BT or ISP issue?
Could the router be faulty?
Anything else I can try.

Thanks.