Well, first of all, all life is composed, ultimately, of non-living matter. Is calcium carbonate organic, or inorganic? What about phosphorus, iron, copper, magnetite, and a host of other inorganic molecules which combine to make up life? All organic molecules ar ecomposed of inorganic elements. And all the elements, minus hydrogen, ultimately, are derived from the processes that create and destroy stars.
RNA and DNA molecules are the givers and organizers of life here on Earth. And those molecule are composed of proteins and amino acids which can be produced in your petri dish, some of the precursors of which have even been discovered in molecule gas clouds in space, as well as some chondrites (stony meteorites). So, PR, if you are looking for ET, all you have to do is search for the remnants of the primordial birth cloud in which the solar system was formed, something NASA is looking for.
Furthermore, I believe I posted a link a while back on a re-examination of the Miller-Urley experiment, which found many more such organic molecules than were first discovered in the original analysis because that analysis lacked the sensitivity of current methods (such as Gas-liquid chromatography-mass spectrometry). So it looks like other biochemists are on the right track. I guess you missed the boat.