Java - Game Development: Issue with multiple keys being pressed all at once

Question

I am a noob coder and I am attempting to make a small 2D Space Shooter game and I have encountered a problem.

I cannot shoot while moving diagonally. This problem also relates to some issues I have when, for example: I start holding up, then begin holding down, then release down but the keylistener for the up key is no longer working so I am no longer moving.

Here is some of my code:

    // This method is called by the KeyInput instance created up above when a key is pressed
public void keyPressed(KeyEvent e)
{
    // Grabbing the key code that was pressed
    int keyCode = e.getKeyCode();

    // Accelerating the player based on key pushed
    if (keyCode == KeyEvent.VK_RIGHT) {
        player.setAccX(player.getAccTick());

    } else if (keyCode == KeyEvent.VK_LEFT) {
        player.setAccX(-player.getAccTick());

    } else if (keyCode == KeyEvent.VK_DOWN) {
        player.setAccY(player.getAccTick());

    } else if (keyCode == KeyEvent.VK_UP) {
        player.setAccY(-player.getAccTick());

    } else if (keyCode == KeyEvent.VK_SPACE) {
        bm.addBullet(new PlayerBullet(player.getX(), player.getY(), this));
    }
}

// This method is called by the KeyInput instance created up above when a key is released
public void keyReleased(KeyEvent e)
{
    // Grabs the key code of the key released
    int keyCode = e.getKeyCode();

    // Sets the accelerationg to 0 based on the key released
    if (keyCode == KeyEvent.VK_RIGHT) {
        player.setAccX(0);

    } else if (keyCode == KeyEvent.VK_LEFT) {
        player.setAccX(0);

    } else if (keyCode == KeyEvent.VK_DOWN) {
        player.setAccY(0);

    } else if (keyCode == KeyEvent.VK_UP) {
        player.setAccY(0);
    }
}

I would like to be able to hold multiple directions at once as well as shoot bullets all at the same time. I know it is not my keyboard because I have played other games just like this and I can hold several keys down and still shoot. Thanks for the help guys!

:D