Can you retrieve an Apple ID with just credit card and phone number details?

Question

My partner, a self-confessed technophobe, has had his iPhone for 18 months - it was set up by his mobile network provider (Orange UK) whose customer support has been worse than useless, keeping him on hold for around 2 hours so far and cutting him off twice.  He's only just bought his first ever computer, at the same time that his iPhone stopped working, before he had time to back up any of his songs, apps etc.  He's just got a replacement iPhone from our local Apple Store but there's no way he can restore his previous purchases as (what he thought was) his Apple ID... isn't.
Because his old phone had v3 software, he apparently never had to input his Apple ID - only the password.  Presumably Orange set him up with an Apple ID (but didn't give him the details) as the only email address he's ever knowingly had isn't recognised as a valid Apple ID.  Try to reset the password by email and the Apple ID system isn't clever enough to spot an unrecognised email address, advising a new password will be emailed with no email ever arriving (not even in junk mail).  (Incidentally, I tried to reset the password on an Apple ID I know isn't valid - my work email address - and it still appeared to have sent a password reminder by email, rather than pointing out the ID doesn't exist!).  Attempting to reset the password by answering the security questions results in the answers being incorrect, which they're most certainly not.  Since he got his original iPhone, he's purchased hundreds of songs on iTunes.  He's clearly been sent receipts somewhere, but we have no idea where.
Apple Store staff are, as usual, brilliant, trying their very best to help, but their hands are tied when it comes to iTunes support, which they tell me is operated as a separate company in its own right (they don't even have access to them by telephone, and iTunes support refuse to talk to me or my partner on the phone).
iTunes support is sending us around in circles, offering up the same tried-and-tested advice time and again, which we've told them many times does not help. They continue to issue the same advice even after sending them a frustrated email headed "PLEASE READ OUR PREVIOUS EMAILS BEFORE RESPONDING!".
I've tried, in vain, to contact iTunes support again about this (they even closed the support ticket even though the issue isn't resolved), and have had no response.
There must be some way Apple can locate my partner's Apple ID if supplied with his credit card details, mobile phone number, billing address and examples of recent purchases?  We've already provided this information to iTunes support but, once again, it's fallen on deaf ears and we've had no response from them.
Can anybody help us get to the bottom of this?  As it stands, he's spent a fortune on hundreds of iTunes songs and apps which he is legally entitled to download, but which he can no longer access, and iTunes support isn't very supportive.
(Incidentally, I recently switched allegiance from 100% Microsoft products to 100% Apple and I'm mightily impressed with their regular customer service, but iTunes support is a completely different animal.)
A million thanks to anyone who can help!

Answer 1

Follow the insrructions here:
Create an iTunes App Store account without a credit card
Note, usually you can't change to a no-payment method but can create a new account that is onlyy good for free apps.