I loaded your module into my dev, there were some install errors but I got through that part to the actual problem you are having. You need to rename your CSS file. The common convention is to name it 'slider.css', since that is the name of your module. It never gets loaded with the 'style.css' though due to your theme probably having the same named stylesheet. Once I changed the name it loaded after clearing the cache. Hope that helps, will post a more detailed explanation when I have a little more time.
Also: See comment about using '#attached' method for this. It would be cleaner.
Original Comment: 'If you are trying to attach CSS that is supposed to show up on a page hen that block is present you should be using 'attached' to load the CSS. Ref: drupal.org/node/2278795'
In your current module code you can use #attach method like below:
// Line 134 of slider.module, make content array and use #markup for content
// Then use #attach method to finish out render array.
$block = array(
'subject' => t('Show Nodes Block'),
'content' => array(
'#markup' => $output,
// Add CSS File with changed name as well.
$block['content']['#attached']['css'] = array(
drupal_get_path('module', 'slider') . '/css/slider.css',