This is very likely a problem:
wp_register_script('jquery17_script', get_template_directory_uri().'/js/jquery-1.7.1.min.js', array('jquery'), '1.0');
You’re enqueueing your own version of jQuery, instead of using the WordPress core-bundled version. To compound the issue, you’re making the core-bundled version of jQuery a dependency, which means that you’re automatically enqueueing both libraries.
That becomes further problematic, here:
wp_register_script('Cycle_script', get_template_directory_uri().'/js/jquery.cycle.all.js', array('jquery'), '1.0');
wp_register_script('slideshow_script', get_template_directory_uri().'/js/slideshow.js', array('jquery'), '1.0');
You enqueue your own jQuery version, and then make the core-bundled version the dependency for your other scripts.
So, I would recommend that you change your entire function like so:
function my_scripts_method(){
// for front page
wp_enqueue_script( 'jquery17' );
wp_enqueue_script( 'Cycle_script', get_template_directory_uri().'/js/jquery.cycle.all.js', array('jquery'), '1.0' );
wp_enqueue_script( 'slideshow_script', get_template_directory_uri().'/js/slideshow.js', array('jquery'), '1.0' );
}
add_action( 'wp_enqueue_scripts', 'my_scripts_method' );
(No need to split the register and enqueue, since you’re doing both at the same time anyway.)
That might fix your entire slideshow problem. If not, there will be something else we need to track down.