Do you mean you have sky broadband ? If so, it is strange that you have an icon on your desktop referring to bt internet. Can you get internet through both of these providers ? If so, you are paying twice for a service you only need once !
If your computer wasn't brand new when you got it, could it just be an icon from a previous user, that doesn't actually do anything which might be why you are having problems using it.
Anyway, as postdog says, once you have your internet connection and a valid email address for yourself, you can email anybody else on the planet, so long as they have a valid email address.