IntelliJ Code Completion not working for new Java classes

Ensure that you are not in Power Save Mode while running IntelliJ (File [menu] -> Power Save Mode checked or not). If Power Save Mode is enabled, IntelliJ will not run background tasks, including code completion.

Make sure you mark all your Source directories as such in File -> Project Structure -> Modules.

For followers, one thing that helped me (auto complete only showed cast field instanceof etc.) was that I had opened a maven module that didn't link correctly to its children (it had a commented out submodules section), so IntelliJ just showed the maven java files as basically "text" files with a tiny "j" in their icon in the project pane. Fixing up the root maven pom.xml file to include the children dirs as modules and voila, they are treated as real java files again, woot!