The way you break into that cycle is to either get popular, become a advertiser or pay a radio promoter. It is illegal to directly pay for play but you can buy airtime and run whatever you want in the commercial spot as long as the quality is met. With that being said, there are other ways to get played on the radio also. You can do drops for Dj's or even show intros. You can also choose stations that are smaller like college and internet stations that play your genre of music. The smaller stations are always looking for new music from the next best thing that is yet to blow.
Outside of trying whats listed above you can also start your own internet radio station so that you can control whats being played. You can be the DJ and the Music Director who makes the decision to play songs. There is a huge fanbase that is waiting for new music and they can be yours. Starting your Own station is a way to reach them. The easy way to start is by using Live365 because they make it easy for you and they even offer a free trial to help you get your station up and going at no charge. Try them out and see.