Player not moving in pygame; no error messages

It’s probably just an indentation error (perhaps pasting to the question), but none of your events are being handled because of the if event.type clauses are not inside the for event loop.

Simply fixing this indentation alleviates this.

The next problem is that you calculate the player_x_change and player_y_change, but never apply the amounts to playerX and playerY.

Since these changes only happen when pygame.KEYDOWN is received, it’s easy to simply add this inside the event handler:

    # Movment
    elif event.type == pygame.KEYDOWN:
        if event.key == pygame.K_a:
            player_x_change -= 10
        elif event.key == pygame.K_d:
            player_x_change += 10
        elif event.key == pygame.K_w:
            player_y_change -= 10
        elif event.key == pygame.K_s:
            player_y_change += 10
        # Move the player
        playerX += player_x_change
        playerY += player_y_change

Note the use of if .. elif. If the event is one particular type, it cannot possibly be another type too (at the same time). This means it’s not necessary to keep re-checking the type. Using elif ("else if") helps with these checks, by stopping the check once a match is found. It is more efficient.

Final code:

import pygame

# Window size
WINDOW_WIDTH    = 400
WINDOW_HEIGHT   = 400
WINDOW_SURFACE  = pygame.HWSURFACE|pygame.DOUBLEBUF
BACKGROUND = (128,  20, 128)


### initialisation
pygame.init()
pygame.mixer.init()
pygame.display.set_caption("Not Moving")

# Game Loop
clock = pygame.time.Clock()
running = True

while running:

    for event in pygame.event.get():
        # Close the game
        if event.type == pygame.QUIT:
            running = False

        # Movment
        elif event.type == pygame.KEYDOWN:
            if event.key == pygame.K_a:
                player_x_change -= 10
            elif event.key == pygame.K_d:
                player_x_change += 10
            elif event.key == pygame.K_w:
                player_y_change -= 10
            elif event.key == pygame.K_s:
                player_y_change += 10
            # Move the player
            playerX += player_x_change
            playerY += player_y_change

        # DON'T REALLY NEED THIS
        #elif event.type == pygame.KEYUP:
        #    if event.key == pygame.K_a:
        #        player_x_change = 0
        #    elif event.key == pygame.K_d:
        #        player_x_change = 0

    # Re-draw the screen
    screen.fill( BACKGROUND )
    player(playerX, playerY)
    pygame.display.update()
    clock.tick(60)                # limit the re-fresh rate to save electricity

pygame.quit()

I also added a frame-rate limiter with a pygame.time.Clock() object, just to save some CPU.