Can you have a degree in journalism and work at a newspaper but then get into marketing without going back to school?

It is possible, if they organization feels that hiring you or moving you into that position makes good business sense. Your going to have to somehow show them that talent. Remember to look at the requirements for the position. If the firm states, a degree in marketing is a requirement, then you have your answer. However, in most cases they will say a bachelor's degree is required etc. In this case you have that opportunity. Still, you will need those marketing skills and somehow convince them you are the best fit for that position.