Hm, I am not aware of any tech, only costing 10 RP, except the ones you start allready researched with, even in a conventional start. Make sure you are not trying to research something, you already know (check the "Available" tick on the research screen (bottom center) _not_ the "All Projects", as this, as the name implies, will list all projects, even those already finished.
Anyway, research and construction finishes only after a construction-cycle, i.e. 5 days per default. Put other techs to research in the queue, so you don´t loose any research points.