That's what I found dumb. I had a problem with NFC in my phone once and they asked me to do the factory reset and I told them I'd do it only if it's last hope (as in I've exhausted all other options). Normally that's the first thing I've noticed people suggest. I would not suggest doing that unless it's absolutely necessary. NFC works fine in my phone now and this is without the reset. However since I live in Toronto, Ontario, Canada, I can just go down to the Apple Store. I still find it funny they asked you to backup and reset, as that specific test can be done without it using diagnostic tools. They tested the NFC on my phone without having me reset my phone to do so.
Further strange is the phone having a SIM Card to activate it. You can set up an iPhone to be a glorified version of an iPod, and then transition it into a phone later. Whoever told you this obviously doesn't know what they are doing. I've set up 2 old Android phones as mini tablets, one of which I was using before I bought an iPhone.
Only if you with a provider will the phone be set up as such. So what @bryansyddall said has a partial truth to it.
However, to set it up as a glorified version of an iPod, you will need a computer. And a WiFi connection.
If you set your phone up this way, with or without the SIM card, the only number you will be able to dial is emergency services (that's mandated by law in the US and Canada).
You can still use your phone, it'll be restored from the last backup made to it.
But I think the ultimate question is, how did it become damaged? They should've replaced it, if there is no damage to your phone at all. If that happened to me, I'd be able to get the phone replaced in Canada. That would be covered under the warranty if they find no damage to the phone itself. And I use an Otterbox Defender case. When I went through the NFC issues, Apple asked me what kind of case I use, and I told them that. They know that the phone will not have any damage at all. And yes, as I mentioned earlier NFC does work on my phone.
Another question: Did they tell you that a pin was damaged or they didn't mention it? Researching this, if a pin is damaged, it won't work. But I am guessing that you treated your phone like a baby. Very carefully. If they didn't do this, I'd take it back and tell them to look harder.
