Issue linking two objects within a <li>

Hey all...
I have a website that I'm working on making updates to. On the homepage is a full page image slider, each with other image elements animating over the main image, which are contained within a <li> item. I am trying to link two of these objects to other pages within the site. When I try, only one of the linked objects will actually have the working link. Any ideas?

The website is http://classicculinaire.com/index.html, and I'm am referring to two of the overlayed image objects on the first slide.

Any help you could offer would be greatly appreciated. I'm pasting the code below for the section I am referring to. The bold, red sections are the images I am trying to link.

<header class="main-header slider-on" id="top">
                <div class="main-slider-container">
                    <div class="main-slider" >
                        <ul class="scrollme">
                            <li data-transition="fade" data-slotamount="7" data-masterspeed="1500" >
                                <img class="rs-parallaxlevel-1" src="img/slider-images/slider-bg4.jpg" alt="Classic Culinaire chef cooking"  data-bgfit="cover" data-bgposition="left top" data-bgrepeat="no-repeat">
                                <div class="tp-caption customin customout rs-parallaxlevel-2"
                                    data-x="center"
                                    data-y="center"
                                    data-voffset="-260"
                                    data-customin="x:0;y:-100;z:0;rotationX:0;rotationY:0;rotationZ:0;scaleX:1;scaleY:1;skewX:0;skewY:0;opacity:0;transformPerspective:1200;transformOrigin:50% 50%;"
                                    data-customout="x:0;y:0;z:0;rotationX:0;rotationY:0;rotationZ:0;scaleX:1;scaleY:1;skewX:0;skewY:0;opacity:0;transformPerspective:600;transformOrigin:50% 50%;"
                                    data-start="1000"
                                    data-speed="1500"
                                    data-easing="Expo.easeOut"
                                    data-elementdelay="0.5"
                                    data-endspeed="600"
                                    data-endeasing="Linear.easeNone">
                                    <img src="img/slider-images/culinary_service.png" alt="Culinary & Service" class="animateme"
                                        data-when="exit"
                                        data-from="0"
                                        data-to="0.3"
                                        data-opacity="0"
                                        data-translatey="-80">
                                </div>
                                <div class="tp-caption customin customout rs-parallaxlevel-2"
                                    data-x="center"
                                    data-y="center"
                                    data-voffset="-25"
                                    data-customin="x:0;y:0;z:0;rotationX:0;rotationY:0;rotationZ:0;scaleX:0.5;scaleY:0.5;skewX:0;skewY:0;opacity:0;transformPerspective:1200;transformOrigin:50% 50%;"
                                    data-customout="x:0;y:0;z:0;rotationX:0;rotationY:0;rotationZ:0;scaleX:1;scaleY:1;skewX:0;skewY:0;opacity:0;transformPerspective:600;transformOrigin:50% 50%;"
                                    data-start="1500"
                                    data-speed="1200"
                                    data-easing="Expo.easeInOut"
                                    data-endeasing="Linear.easeNone">
                                    <img src="img/slider-images/mealdelivery.png" alt="Excellence" class="animateme"
                                        data-when="exit"
                                        data-from="0"
                                        data-to="0.4"
                                        data-opacity="0"
                                        data-translatey="-70">
                            
                                </div>
                                
                                <div class="tp-caption customin customout rs-parallaxlevel-2"
                                    data-x="center"
                                    data-y="center"
                                    data-voffset="155"
                                    data-customin="x:0;y:80;z:0;rotationX:0;rotationY:0;rotationZ:0;scaleX:1;scaleY:1;skewX:0;skewY:0;opacity:0;transformPerspective:1200;transformOrigin:50% 50%;"
                                    data-customout="x:0;y:0;z:0;rotationX:0;rotationY:0;rotationZ:0;scaleX:1;scaleY:1;skewX:0;skewY:0;opacity:0;transformPerspective:600;transformOrigin:50% 50%;"
                                    data-start="2700"
                                    data-speed="700"
                                    data-easing="Expo.easeOut">
                                    <img src="img/slider-images/chefservices.png" alt="Cooking Since" class="animateme"
                                        data-when="exit"
                                        data-from="0"
                                        data-to="0.5"
                                        data-opacity="0"
                                        data-translatey="60">
                                </div>
                              
                                <div class="tp-caption customin customout rs-parallaxlevel-2"
                                    data-x="center"
                                    data-y="center"
                                    data-voffset="300"
                                    data-customin="x:0;y:40;z:0;rotationX:0;rotationY:0;rotationZ:0;scaleX:1;scaleY:1;skewX:0;skewY:0;opacity:0;transformPerspective:1200;transformOrigin:50% 50%;"
                                    data-customout="x:0;y:0;z:0;rotationX:0;rotationY:0;rotationZ:0;scaleX:1;scaleY:1;skewX:0;skewY:0;opacity:1;transformPerspective:600;transformOrigin:50% 50%;"
                                    data-start="4000"
                                    data-speed="800"
                                    data-easing="Power2.easeInOut">
                                    <a href="http://classicculinaire.com/contact.html" class="custom-button button-style1 animateme"
                                        data-when="exit"
                                        data-from="0"
                                        data-to="0.6"
                                        data-opacity="0"
                                        data-translatey="60"><i class="icon-eye"></i>Contact us today!</a>
                                </div>
                              
                            </li>

HTML:

Thanks!
David

 

Not to sure if this will help, but give this a try...

<a href="Your Link"><img src="img/slider-images/culinary_service.png" alt="Culinary & Service" class="animateme"
                                        data-when="exit"
                                        data-from="0"
                                        data-to="0.3"
                                        data-opacity="0"
                                        data-translatey="-80"></a>

Code (markup):