Why won't my GUI display, running via NetBeans

Both of your files have this

public static void main(String[] args) 
{  
    new TestGUI3();  
}  

Which is going to call the default constructor for the TestGUI3 class, which does nothing.

Additionally, you seem to be conflicting your understanding of constructors with instance methods.

public void TestGUI3(NewGameGUI NewGameGUIMethod)

and

public void NewGameGUIMethod()

Constructors do not have a return type. Plus, the second of these isn't even the name of the class it is in...

I would recommend you do something like class TestGUI3 extends JFrame implements ActionListener, and that way, you don't need to have an inline reference to a Frame, and instead your classes are a Frame that you can setVisible() on to show them.

1-remove void because adding it will make it normal method not constructor public void NewGameGUIMethod() , also it should be named NewGameGUI , the final name would be public NewGameGUI()
2- remove void in the other class, for the same of above public void TestGUI3(NewGameGUI NewGameGUIMethod), also there is no need to pass NewGameGUIMethod as paramter since it is not used in TestGUI3
3- You are constructing a new frame everytime you call the NewGameGUIMethod() , which cause a recursion, just comment the frame creation , and set the instance you constructed to visible as follows:

    //NewGameGUI test = new NewGameGUI();
    //test.setFrame(f2);
    f2.setVisible(true);

4- update the main method of NewGameGUI to be :

public static void main(String[] args) {
    new NewGameGUI();
}

Full class code for NewGameGUI class:

package test.q5;

import java.awt.event.*;
import javax.swing.*;
import javax.swing.JOptionPane;
import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.JLabel;

public class NewGameGUI implements ActionListener {
    JRadioButton rb1, rb2, rb3, rb4, rb5, rb6, rb7, rb8, rb9, rb10, rb11, rb12, rb13, rb14, rb15, rb16, rb17, rb18, rb19, rb20;
    JFrame f2;
    JButton b;
    JLabel label1;

    public  NewGameGUI() {
        label1 = new JLabel("Please choose a team");
        f2 = new JFrame("Ballon d'or");
        f2.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        rb1 = new JRadioButton("Arsenal");
        rb2 = new JRadioButton("Aston Villa");
        rb3 = new JRadioButton("Bournemouth");
        rb4 = new JRadioButton("Chelsea");
        rb5 = new JRadioButton("Crystal Palace");
        rb6 = new JRadioButton("Everton");
        rb7 = new JRadioButton("Leicester City");
        rb8 = new JRadioButton("Liverpool");
        rb9 = new JRadioButton("Manchester United");
        rb10 = new JRadioButton("Manchester City");
        rb11 = new JRadioButton("Newcastle United");
        rb12 = new JRadioButton("Norwich City");
        rb13 = new JRadioButton("Southampton");
        rb14 = new JRadioButton("Stoke City");
        rb15 = new JRadioButton("Sunderland");
        rb16 = new JRadioButton("Swansea City");
        rb17 = new JRadioButton("Tottenham Hotspur");
        rb18 = new JRadioButton("Watford");
        rb19 = new JRadioButton("West Brom");
        rb20 = new JRadioButton("West Ham");

        label1.setBounds(50, 25, 200, 30);
        rb1.setBounds(50, 100, 170, 30);
        rb2.setBounds(50, 150, 170, 30);
        rb3.setBounds(50, 200, 170, 30);

        ButtonGroup bg = new ButtonGroup();
        bg.add(rb1);
        bg.add(rb2);
        bg.add(rb3);
        bg.add(rb4);
        bg.add(rb5);
        bg.add(rb6);
        bg.add(rb7);
        bg.add(rb8);
        bg.add(rb9);
        bg.add(rb10);
        bg.add(rb11);
        bg.add(rb12);
        bg.add(rb13);
        bg.add(rb14);
        bg.add(rb15);
        bg.add(rb16);
        bg.add(rb17);
        bg.add(rb18);
        bg.add(rb19);
        bg.add(rb20);

        b = new JButton("OK");
        b.setBounds(200, 250, 180, 30);
        b.addActionListener(this);
        f2.add(rb1);
        f2.add(rb2);
        f2.add(rb3);
        f2.add(rb4);
        f2.add(rb5);
        f2.add(rb6);
        f2.add(rb7);
        f2.add(rb8);
        f2.add(rb9);
        f2.add(rb10);
        f2.add(rb11);
        f2.add(rb12);
        f2.add(rb13);
        f2.add(rb14);
        f2.add(rb15);
        f2.add(rb16);
        f2.add(rb17);
        f2.add(rb18);
        f2.add(rb19);
        f2.add(rb20);
        f2.add(b);

        f2.setSize(500, 500);
        f2.setLayout(null);
        f2.setVisible(true);

        //NewGameGUI test = new NewGameGUI();
        //test.setFrame(f2);
        f2.setVisible(true);

    }

    public void setFrame(JFrame f2) {
        this.f2 = f2;
    }

    public JFrame getFrame() {

        return f2;
    }

    public void actionPerformed(ActionEvent e) {
        if (rb1.isSelected()) {
            f2.dispose();

            // JOptionPane.showMessageDialog(f,"New Game");
        }
        if (rb2.isSelected()) {
            JOptionPane.showMessageDialog(f2, "Load Game");
        }
        if (rb3.isSelected()) {
            System.exit(0);
        }

    }

    public static void main(String[] args) {
        new NewGameGUI();
    }
}

Class 2:

package test.q5;

import java.awt.event.*;
import javax.swing.*;
import javax.swing.JOptionPane;
import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.JLabel;

public class TestGUI3 implements ActionListener {
    JRadioButton rb1, rb2, rb3;
    JFrame f;
    JButton b;

    public  TestGUI3() {
        f = new JFrame("Welcome to Ballon d'or");
        f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        rb1 = new JRadioButton("Start New Game");
        rb2 = new JRadioButton("Load Game");
        rb3 = new JRadioButton("Quit");

        rb1.setBounds(50, 100, 170, 30);
        rb2.setBounds(50, 150, 170, 30);
        rb3.setBounds(50, 200, 170, 30);

        ButtonGroup bg = new ButtonGroup();
        bg.add(rb1);
        bg.add(rb2);
        bg.add(rb3);

        b = new JButton("OK");
        b.setBounds(200, 250, 180, 30);
        b.addActionListener(this);
        f.add(rb1);
        f.add(rb2);
        f.add(rb3);
        f.add(b);

        f.setSize(500, 500);
        f.setLayout(null);
        f.setVisible(true);
    }

    @Override
    public void actionPerformed(ActionEvent e) {
        if (rb1.isSelected()) {
            f.dispose();
            NewGameGUI test = new NewGameGUI();

            test.getFrame().setVisible(true);
            // JOptionPane.showMessageDialog(f,"New Game");
        }
        if (rb2.isSelected()) {
            JOptionPane.showMessageDialog(f, "Load Game");
        }
        if (rb3.isSelected()) {
            System.exit(0);
        }

    }

    public static void main(String[] args) {

        new TestGUI3();
    }
}

Final note : you should consider reading about swing layouts(FlowLayout,BorderLayout,GridLayout,BoxLayout) to be able to control your components correctly.