I think Apples have a one year guarantee, don't they? Am uncertain, but I'm sure that your Apple store would help you out.
Hope the weather improves for you. We are currently experiencing a deliciously chilly winter, which in Melbourne means nights of 4-5C or so. I love our winter!
I found out an interesting bit of trivia - my brother, who is currently living in Berlin, tells me that wlan is what we refer to as wifi.
Your mother seems extraordinarily robust and spirited for her age - was astonished to hear that she was exploring the Schloss, steps and all. Graz sounds fascinating.