A couple of questions.....

1. Where does the domestic phone system end and the network begin?

2. At what point does the repair become the responsibility of the network provider?

The master socket is usually the demarc point - ie. the one where the wire from outside terminates.

Normally everything line-side of that is the providers, everything premises-side is the subscriber. Unless you chopped the cable outside with a hedgetrimmer etc in which case brace yourself for a possible (hefty) charge.

Do you have an NTE5?

http://www.telephonesuk.co.uk/images/NTE5_BT_front.jpg
http://www.telephonesuk.co.uk/images/NTE5_BT_rear.jpg

if you remove the lower plate with the socket on, anything attached to that plate is your responsibility. The wiring on the other larger plate with the BT logo on is BT's responsibility and you're not allowed to touch it. If you have problems with your phone or ADSL the usual practice is to remove that lower plate and plug a modem or phone into the socket behind that place, which disconnects your wiring and if the fault is still there it tells you it's BT or your equipment.

BT will repair anything up to their part of the NTE5 for free if it's at fault. If it's your equipment or wiring you'd be charged for a callout and/or any remedial work.

Not sure what the case is on non-NTE5 lines.

Exactly the same, apart from there is no lower half. The network and subscribers cabling is connected to the same connections. BT look after the network cables and the master socket. Any extensions connected are your responsibility.