Asexuality is, in its basic definition, not experiencing sexual attraction. It is an orientation, just as heterosexuality, homosexuality, bisexuality, etc, so there are a lot of different things under that label that people can do and experience. Within the orientation, some have libidos and some do not. Some engage in sexual acts and some do not. The thing is, libido is the basic urge and is controlled by hormones in the body (said to be a general feeling like hunger), sexual attraction is triggered by other people, so they can work independantly of each other. Sexual acts are a behaviour and asexuals can have sex for a number of reasons, including curiosity, peer pressure, compromise with a romantic partner, to have children, or because they find it feels good either physically or emotionally. Sex can happen without sexual attraction- some heterosexual people experiment homosexually for whatever reason (and presumably vice versa) and many homosexuals over the centuries have successfully engaged in heterosexual acts (albeit out of societal necessity).

If you don't experience sexual attraction and don't have a libido, you can still be asexual, it just makes you what we would call a "nonlibidoist asexual" to be more precise. Since asexuality is an orientation, not just a trait, there are a wide range of experiences and possibilities within it. I had hoped that AVEN might give you some answers, but perhaps that site isn't the right crowd for you.

Of course, what you label yourself or don't label yourself is your own decision, but under the definition of asexuality you would qualify as asexual.