Amalgamate two toggle functions into one
function toggleVisibility() {
    var temp = document.getElementById('regStart').style.visibility
    document.getElementById('regStart').style.visibility = document.getElementById('regPage').style.visibility;
    document.getElementById('regPage').style.visibility = temp;

    var suffix = "Gray.png";
    if ( 'hidden' === temp ) {
        suffix = "Depressed.ico";
    }

    document.getElementById('facebook').src = "/images/js project/Facebook" + suffix;
    document.getElementById('google').src = "/images/js project/Google" + suffix;
    document.getElementById('winlive').src = "/images/js project/WinLive" + suffix;
    document.getElementById('yahoo').src = "/images/js project/Yahoo" + suffix;
}


The first insight is that you want to swap the visibility settings for regStart and regPage.  So use the normal swap format with a temp variable.  

The second insight is that your image paths have the same start for both cases of each image.  So the beginning can be a constant value for each image. 

The third insight is that your image paths have the same ending for all images in a particular case.  So based on the value of temp (arbitrarily chosen as the shortest variable name), change the ending.  

I also normalized the indentation.  It was inconsistent in your original functions.