Phone line engaged

[#1]

I am unable to use my home phone, there is no dial tone. I have been through the checks as per the video. When I phone in to my landline number on my mobile I get an engaged tone, then it drops out. When my wife does the same on her phone she gets a message that the line is engaged.
This morning road resurfacing started close to the BT phone distribution box. This may or may not have a bearing on the problem, my next door neighbour's phone is accepting calls, since he is not in I cannot check whether or not he can dial out. I have tried the link to report a problem online, it just refreshes the page since it is the same url that I am already on.
I have tried phoning the support help line but when I get through there is a message that all the lines are busy and that there is a 15 minute wait. On a pay per use phone this would be too expensive.
What now?

[#2]

If you disconnect your phone from the socket and disconnect the test socket plate on the master socket, does the phone line still appear to be engaged ?
If it does then it is most likely a line fault and will need to be logged as either a fault through the ticket system on the members portal or a phone call to PN to report the issue.
There are various numbers available for reporting the problem - some may be cheaper than others from your mobile if it helps ?
0800 432 0200 or 0345 140 0200

[#3]

Hi BillBoddy,
I've just taken a look at your account and can see the next step to investigate the fault would involve an engineer visit.
I've just tried calling your mobile so we could discuss this whilst I have a view of the available appointments but the call wouldn't connect for some reason.
Please give us a call when you can and we'll arrange the soonest available engineer slot that's convenient for you.

[#4]

Call arranged for BT to come to research fault. The engineer did not arrive within the specified time, when he did come an hour and a half late I was out. Then was told that the most likely reason for this would be a short between the two wires used by the phone. Found the short, replaced the faulty part of the cable, now working again.
You can buy a multimeter for under £10 which is way below what Plusnet, BT or an external phone will charge. Then you need a punchdown tool for even less.

[#5]

Glad you got it sorted
The problem with DIY fixes is that you can only work on the bit of wire inside your house *after* the master socket. If you mess it up then you get charged. It is technically against the law to mess with the master socket or any of the wiring between the socket and the exchange otherwise I'm sure there would be lots of frustrated customers fixing their own lines 
Was the fault internal to your property or outside (our of curiosity) ?

[#6]

In basic terms, if it connects to the faceplate, it's yours, if it's to the test socket and beyond, hands off...
(though I will admit to moving master sockets about in the past myself, but doing it with the proper tools in the proper manner, collecting vintage telephones helps to learn about how it's done and what not to do!)