Is opening a store for selling and renting video tapes, while adhering to Sharia teachings and avoiding violations, considered haram, or would the earnings derived from it be haram?

Video, radio, and television are tools that cannot be described as either permissible or forbidden in themselves. Rather, it is their usage that is described as such. If they are used for what is purely forbidden or predominantly forbidden, then they are forbidden. Otherwise, they are permissible. So, if they are used for good, they are good, and if not, they are evil.