My phone does not ring

[#1]

Yikes, you're certainly right about the ring voltage - 90V AC @ 20Hz applied over the 50V DC normally present according to Wikipedia. I'm not sure about the bell wire as my experience of telephone wiring has always included filters but I'm struggling to understand how my phones ring without a bell wire when filters are included, as opposed to if they weren't?

[#2]

In the older days before the modern phone sockets and the phones had  electro-mechanical  bells when you had extension if the wiring was not modified then with a Loop Disconnect Dialling the bells in the other phones would tinkle. To overcome this problem one of the phones was made the master phone and the ringing circuitry was use to feed the other phones. The master phone and the extension phones internal wiring had to be modified in addition to the junction box that was screwed to the wall feeding each phone.
As this system required knowledge of telephony it was not something the home owner could do. So when the new socket system was devised they remove the ringing circuit from the phones and placed it into the master socket and the phones produced at this time did not have any of the ringing circuit included. Roll on a few more years when phones no longer use loop disconnect dialling but DTMF and electro-mechanical bells are not used any more and some phone handset manufacturers reintroduced the ring circuit, especially DECT phones as these are self powered.
As for ADSL filters these are fitted with the ring circuit hence the reason why pin 3 can be disconnected and the phone will ring.

[#3]

I also have a non - ringing phone.  (see  http://community.plus.net/forum/index.php/topic,108234.0.html )
In my case it's almsot certainly due to a mis-wire done at install time.
A few things to try in turn (some you may have done ...as I read back, but good to summarise for other who read later)
[make sure you use a known working phone, pref two known working phones ... not DECT]
1: Do use 17070 to test the ring each time  (don't hangup too quick ... but you can hit one without waiting for the voice)
2: If you are on a wired extension ... test this 1st
3: Next move to the front socket of the NTE5 box ... do 17070 test
4: lastly remove the front panel of the NTE5 , behind it is ANOTHER phone socket, carry out the test there

If the last one does not work .. your socket is fundamental broken/mis-installed  ... if 4 works but one of the other fails, it 'your' wiring problem
(as in if you call BT , you pay for it 🙂 )

[#4]

Good advice vetterlein, I hope you get that sorted out soon.
Adam

[#5]

There is one exception to your last case..
If the test socket behind the NTE5 faceplate works, but not from the NTE5 faceplate's test socket,  it could be that the faceplate itself is damaged. 
I had this situation last year after a nearby lightning strike,  fibre connection was fine,  but phone wasn't  (no ring when called,  and no dial tone!).

[#6]

And another possibility to option 4 - Or the faceplate not fitting correctly. I came across a case of this recently, it appeared to be due to the test socket/capacitor/surge suppressor assembly not sitting correctly on the backplate (more recent Openreach NTE5a).
Edit: I also came across a case a while back where the contacts in the test socket had become misaligned.