KeyListener not responding in Java swing

I am making a game and I have a Main Menu that works great. When I select one of the options, it brings up another menu in a new window. However, in this new window, the KeyListener is not responding. If I return to the main menu window, KeyListener still works. Here is the code:

MainMenu:

import java.awt.*;
import java.awt.event.*;
import java.awt.image.*;
import javax.swing.*;
import java.io.*;
import javax.imageio.*;

public class DisplayMainMenu extends JFrame implements KeyListener{

  static int width = 799, height = 463;
  int arrowPos = 310;
  boolean clear = true;
  BufferedImage menu = null;
  BufferedImage arrow = null;
  LevelSkip test = new LevelSkip();
  boolean done = false;
  static DisplayMainMenu main;

  public static void main(String[] args){
    main = new DisplayMainMenu();
    main.setResizable(false);
    main.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    main.setVisible(true);
    main.init();
  }

  public void init() {
    try{
      menu = ImageIO.read(new File("Main Menu.png"));
      arrow = ImageIO.read(new File("arrow.png"));
    }catch(IOException ie) {
      System.out.println(ie.getMessage());
    }
    this.setSize(width, height);
    this.addKeyListener(this);
    clear = true;
    paint(getGraphics());
  }

  public void paint (Graphics g){
    if(clear==true){
      g.drawImage(menu,0,0,null);
      clear = false;
    }
    g.drawImage(arrow,275,arrowPos,null);
  }
  public void keyPressed(KeyEvent e){
    String key = e.getKeyText(e.getKeyCode());
    if(key == "Up"){
      clear = true;
      if (arrowPos > 310)
        arrowPos -= 30;
      else
        arrowPos = 370;
      paint(getGraphics());
    }
    if(key == "Down"){
      clear = true;
      if (arrowPos < 370)
        arrowPos += 30;
      else
        arrowPos = 310;
      paint(getGraphics());
    }
    if(key == "Space"){
      done = true;
      switch(arrowPos){
        case 310:  System.out.println("RUN NEW GAME"); test.init();
          break;
        case 340:  System.out.println("RUN HIGH SCORES");
          break;
        case 370:  System.exit(0);
      }
    }
  }
  public void keyReleased(KeyEvent e) {}
  public void keyTyped(KeyEvent e) {}
}

LevelSkip:

import java.awt.*;
import java.awt.*;
import java.awt.event.*;
import java.awt.image.*;
import javax.swing.*;
import java.io.*;
import javax.imageio.*;

public class LevelSkip extends JFrame implements KeyListener {

  static int width = 799, height = 463;
  int arrowPos = 109;
  boolean clear = true;
  BufferedImage menu = null;
  BufferedImage arrow = null;

  public void init() {
    LevelSkip main = new LevelSkip();
    main.setSize(width, height);
    main.requestFocusInWindow();
    main.addKeyListener(main);
    main.setResizable(false);
    main.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    main.setVisible(true);
    try{
      menu = ImageIO.read(new File("level skip.png"));
      arrow = ImageIO.read(new File("arrow2.png"));
    }catch(IOException ie) {
      System.out.println(ie.getMessage());
    }
    clear = true;
    paint(main.getGraphics());
  }

  public void paint (Graphics g){
    if(clear==true){
      g.drawImage(menu,0,0,null);
      clear = false;
    }
    g.drawImage(arrow,arrowPos,355,null);
  }
  public void keyPressed(KeyEvent e){
    String key = e.getKeyText(e.getKeyCode());
    if(key == "Left"){
      clear = true;
      if (arrowPos > 109)
        arrowPos -= 260;
      else
        arrowPos = 629;
      paint(getGraphics());
    }
    if(key == "Right"){
      clear = true;
      if (arrowPos < 629)
        arrowPos += 260;
      else
        arrowPos = 109;
      paint(getGraphics());
    }
    if(key == "Space"){
      switch(arrowPos){
        case 109:  System.out.println("ADD 1 TO LEVEL AND RUN BATTLE");
        break;
        case 369:  System.out.println("ADD 5 TO LEVEL AND RUN BATTLE");
        break;
        case 629:  System.out.println("ADD 10 TO LEVEL AND RUN BATTLE");
      }
    }
  }
  public void keyReleased(KeyEvent e) {}
  public void keyTyped(KeyEvent e) {}

}

I'm not quite sure what the problem is, the skip level window is displayed normally, it just does not register keystrokes.