I suspect your problem is the card, not the camera. Even a bit of, say, sun exposure could deform the card shell to the point that it will not fit in the camera properly, but you cannot see the problem with the card.
It was inserted correctly, I'm assuming. Correct insertion comes with a solid 'click' as I'm sure you know, and you hear another click when you push the card in to remove it. I would try to (carefully) extract it with tweezers - try pushing it in first with the tweezers before you pull - and test another card. If you cannot remove it without obviously damaging the camera or if another card you try also gets stuck, get it looked at. I would not attempt to open the camera especially if it is under warranty (which it should be after only 5 months).
From what I can see, there would be no way to access the internals of that part of the camera without disassembling the whole device. The two screws inside the door merely hold the door in place.
can you move it at all? how about forcing it out maybe pulling with a pair of tweezers? or maybe needle nose pliers, it would be a pain to have to send it in for something that simple.