Broken Sleep/Lock button

So my sleep/lock button recently "broke". It's there, but it's functioning half of the time, and it's extremely difficult to press it. I took it in to my carrier, and they said they'd take a look at it.

Yesterday I got an email that they won't replace it, because I've also got a cracked screen, and that the lock button have suffered damage from this (I can tell you it has not, because the lock button was fine until 2 weeks ago, and I've had that crack for over a half year) and so they won't give me a replacement nor will they repair it (It's non-repairable they say), because it's not under the guarantee.

I haven't picked my phone up from the store yet, but I think they told me (when I sent the phone in for a check-up) that if I didn't agree with their decision, I could contact Apple in some way, and they'd have a look at it.

What is Apple's policy on this? Will they also use the same explanation, or will they actually see that it's 2 different problems that occurred at different dates. This is the second time something like this happens to me with this carrier, and it's quite annoying.

Anyone got any advice from me? PS. I'm from Denmark

 

Thanks to you both for the advice... I'm not really sure if there is an official Apple store in Denmark, but I'll sure research this some more.

Have a good day