In database, it stores the date details with prefix as _start and _end so you need to change the meta keys accordingly. Please have a look at the below code.
<p>Start time details</p>
<p>Date: <?php echo get_post_meta($post->ID, '_start_day', true);?>.<?php echo get_post_meta($post->ID, '_start_month', true);?>.<?php echo get_post_meta($post->ID, '_start_year', true);?></p>
<p>Hour: <?php echo get_post_meta($post->ID, '_start_hour', true);?>:<?php echo get_post_meta($post->ID, '_start_minute', true);?></p>
<p>End time details</p>
<p>Date: <?php echo get_post_meta($post->ID, '_end_day', true);?>.<?php echo get_post_meta($post->ID, '_end_month', true);?>.<?php echo get_post_meta($post->ID, '_end_year', true);?></p>
<p>Hour: <?php echo get_post_meta($post->ID, '_end_hour', true);?>:<?php echo get_post_meta($post->ID, '_end_minute', true);?></p>
In case $post->ID does not contain a value, try using get_the_ID().