@Tim2247 The protocol when you arrive to find a place unacceptable is to first contact the host, giving them an opportunity to remedy the situation, and if that isn't possible, or the host refuses or doesn't care, to call Airbnb to cancel right away, stating that the place is inaccurately described, lacks the amenities shown and described in the listing, etc.
If this is what you did, then you'll just have to try contacting customer service again- it's a sad fact that you'll get a completely different respnse from one CS rep than another, so you just have to be persistent until you get an understanding, helpful rep. No, Airbnb will seldom contact you- you could easily die holding your breath on that one. You could try contacting them through their Twitter account-that is said to get better responses.
If you do get a refund, be aware that it will probably only be for unstayed nights of the booking, although personally I think you are entitled to more back than that, due to the circumstances.
Did it say anywhere in the listing that there was no cell service at the house? One thing I'll say is that it's never a good idea to assume anything with an Airbnb, since they are all so different- a guest should certainly be able to assume that the place is accurately described, but assuming that there is cell reception isn't a good idea if you are reliant on it, as most people are to some degree, and you to a large degree. This holds true for many assumptions re Airbnbs- if someone is allergic to dogs, for instance, just because a listing says "No pets" doesn't mean the owner doesn't have a dog (altho most hosts will mention that in their listing info), it just means they don't accept guest pets. So if a guest is allergic, they should always take responsibility for their own health and double check before booking.