Okay, let’s try something.
Open up the wp-content/plugins/ajax-search-pro/ajax-search-pro.php file and go to line 13, where you should see this:
[php]
define("ASP_PATH", plugin_dir_path(__FILE__));
[/php]
change that line to:
[php]
define("ASP_PATH", untrailingslashit(plugin_dir_path(__FILE__)) );
[/php]
Now try to activate the plugin again, if it throws the same error message, then it’s something else. Copy/pase the error message you get after this change.