And they'll find ... Alien noise (encryption)
Any civilization sufficiently advanced enough to radiate signals is also going to be sufficiently advanced to encrypt their communications. We could be pulling in all sorts of alien communications right now. Since the best encryption makes its signal indistinguishable from noise, there's no way that we are going to know that it's there.
It's happening to our civilization already. For example, the Nintendo DS that my kids play with uses RSA encryption for PictoChat.