In both your queries you are doing it wrong. You are running a separate instance of WP_Query
for every argument set
$args = array( 'posts_per_page' => $count, // Limit count );
$query = new WP_Query( 'cat=1' );
$query = new WP_Query( $args );
Should be
$args = array( 'posts_per_page' => $count, 'cat' => 1 );
$query = new WP_Query( $args );