Try creating a class named overlay and apply the following css to it:
a.overlay { width: 100%; height:100%; position: absolute; }
Make sure it is placed in a positioned element.
Now simply place an <a> tag with that class inside the div you want to be linkable:
<div id="buttonOne">
<a class="overlay" href="......."></a>
<div id="linkedinB">
<img src="img/linkedinB.png" alt="never forget the alt tag" width="40" height="40"/>
</div>
</div>
PhilipK's suggestion might work but it won't validate because you can't place a block element (div) inside an inline element (a). And when your website doesn't validate the W3C Ninja's will come for you!
An other advice would be to try avoiding inline styling.