I am using WordPress version 3.4.2 with Responsive Theme by ThemeID version 184.108.40.206.
To modify content on the Home Page you must place it in the Featured Content area of the Home Page area of Theme Options as explained here:
When I put in my WowSlider short code [wowslider id="1"] I only see the text for the short code as you can see here on my page:
I tried it on a regular page and it works fine:
I also tried entering the code suggested by wowslider here http://wordpress.org/extend/plugins/wowslider/ for a widget, which is <?php wowslider(1); ?>, but that did not work either.