This week's book giveaway is in the OO, Patterns, UML and Refactoring forum. We're giving away four copies of Refactoring for Software Design Smells: Managing Technical Debt and have Girish Suryanarayana, Ganesh Samarthyam & Tushar Sharma on-line! See this thread for details.
Please post an SSCCE. Right now I get compiler errors about missing class "Screen". Since that's doing the actual full screen handling we can't test anything.
That said, overriding the paint method is the AWT way to go. In Swing you override paintComponent. However, JFrame (and JWindow and JDialog) don't have that method; instead you should set its content pane to be some container (usually JPanel) that does override paintComponent.