<a id="my_link" href="https://vk.com/durov" target="_blank" style="display: none;">
<img src="img/57d3d0a9e386c157136717cc.png" width="30px"/>
</a>
<input type = "button" onclick = "document.getElementById('my_link').style.display = 'inline';" value = "связаться со мной" />