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Welcome to the forum. You will be charged if an engineer calls and finds the problem is caused by your equipment and not Openreach's, or if damage has been caused on your property. Damage aside, any fault up to and including the master socket is down to Openreach, anything your side is your responsibility.
The helpdesk warning is given so that customers cannot claim they were unaware there would be a charge if their equipment is faulty; it does not mean you will automatically be charged. It sounds as though there is a line fault, but you can check by connecting a phone to the test socket behind the master socket faceplate. If there's still no dial tone the fault is on the Openreach side.
BT Retail are just making you aware of the [Openreach] Engineer Callout Charge if the fault is found within your property (ie your internal wiring or an issue with your equipment) or damage to your property as this your responsibility
You should not be charged if the fault is external ie on the Openreach "Last Mile" infrastructure or within the exchange.
To Test whether the fault is within your responsibilty or if it is on the Openreach or BT Retail side of things is to connect your landline phone into your TEST Socket.
The TEST socket if found behind the removable faceplate of the BTNTE5 Master socket (see image below for clarification)
If there is still no dial tone whle connect to the TEST socket and that you have tried another handset, then the fault will more likely be Openreach's and BT Retails responsibilty.
If there is a dail tone present when connect to the TEST socket, then it may well be an issue with your internal wiring and therefore may be charged the Engineer Callout Charge.
You will have to accept that you are aware of the Engineer Callout Charge if the fault is found within the boundaries of your responsibility to have an engineer come out to your property for futher investigation.
Have a look at this guide here on troubleshooting the phone fault to make sure that the fault is external: http://bt.custhelp.com/app/answers/detail/a_id/9812
Here is some info about the Engineer Callout Charge http://bt.custhelp.com/app/answers/detail/a_id/12439/c/345
Edit: Sorry pottyperson has also posted the same info