House alarm interferes with phone line, what could the problem be?

I bought a house with an ADT alarm which is connected to the phone line, the phone has stopped working and bt have said it is something to do with the alarm, my broadband still works though which is strange. I have called ADT and they want to charge me for an engineer to come and fix it but why should I pay them when I didn't buy the alarm and neither have I used it ever, please could someone tell me what the problem could be and thanks in advance for any assistance you may give me.