Slider do not add alt attribute. Cant get alt attribute from a media library!

When I test get_the_post_thumbnail (also the_post_thumbnail) on WordPress 3.5.1, the alt attribute is added as it should be. If you look at the source, you will see that get_the_post_thumbnail uses wp_get_attachment_image which does add that alt attribute. By default, that attribute is the image file name but it can be edited from wp-admin->Media to be anything you want.

Either:

1. A plugin or your theme has already altered the output of get_the_post_thumbnail, possibly via the post_thumbnail_html filter, though I did notice other filters in the code, or
2. Your slider or theme template doesn’t work the way you think it does. Perhaps it isn’t using get_the_post_thumbnail, for example.

It is difficult to say more, or to say exactly where this is going wrong, without seeing the relevant code.

Also, get_the_post_thumbnail function is not a pluggable function so I have to assume you are trying to hack a Core file, which you should not be doing.

Edit:

In the latest bit of code you posted, you can see the section that generates the image tag:

<a href="https://wordpress.stackexchange.com/questions/97571/<?php the_permalink(); ?>"><img src="<?php echo $image ?>"/></a>

It isn’t WordPress at all, but a customized bit of code. That is where you need to add the alt attribute.

<a href="https://wordpress.stackexchange.com/questions/97571/<?php the_permalink(); ?>"><img src="<?php echo $image ?>" alt="I am so alt it hurts!" /></a>

You can create the alt attribute manually or copy the code from wp_get_attachment_image

$default_attr = array(
    'src'   => $src,
    'class' => "attachment-$size",
    'alt'   => trim(strip_tags( get_post_meta($attachment_id, '_wp_attachment_image_alt', true) )), // Use Alt field first
);
if ( empty($default_attr['alt']) )
    $default_attr['alt'] = trim(strip_tags( $attachment->post_excerpt )); // If not, Use the Caption                    
if ( empty($default_attr['alt']) )
    $default_attr['alt'] = trim(strip_tags( $attachment->post_title )); // Finally, use the title

Or cook up your own function for creating the alt attribute.