Nymox, if you pay the wire maintenance fee (check your bill) all fault finding is free up to the point where they work out what the problem is. So you could tryin ringing Residential faults, tell them all about it (tell them you've already spoken to broadband helpdesk and done all they've told you) and see if they will send someone out to check the line. Depending if you are home or not, the tech would test it with their laptop in the house. If you don't pay wire maintenance then you will pay the fees on the link but it shouldn't be what you mentioned as far as I know (I worked there long ago).
from here http://www.telecom.co.nz/content/0,8748,205402-1007,00.html