How do I display an image before the first post of the loop when I'm using get_template_part?

The variable $count is accessible in the scope of the current function only. So whatever happens inside get_template_part() cannot know that variable.

You could use a global variable, which is accessible everywhere as $GLOBALS['count']. But then you risk collisions with plugins and maybe other code.

I recommend a helper function for the functions.php:

/**
 * Remember a number.
 *
 * @param  int|FALSE $add A number to add, or FALSE to reset the counter to 0 (zero).
 * @return int
 */
function wpse_count( $add = 0 )
{
    static $counter = 0;

    if ( FALSE === $add )
        $counter = 0;
    else
        $counter += (int) $add;

    return $counter;
}

You can use that function to remember any number you want. In your example that should look like this:

<?php 
// Reset the counter
wpse_count( FALSE );

if ( have_posts() ) : // Start the Loop

    while ( have_posts() ) : 
        the_post();
        wpse_count( 1 );
        get_template_part( 'content', get_post_format() );
    endwhile;

endif; 
?>

And in the template part file you print the value without adding anything:

echo wpse_count();

Example in TwentyEleven’s content-status.php

<?php 
the_content( __( 'Continue reading <span class="meta-nav">&rarr;</span>', 'twentyeleven' ) ); 
echo 'Number: ' . wpse_count();
?>

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