Links aren't clickable. Anchors not working

Links aren't clickable. Anchors not working

I have anchor links on icons for social media at the top of my page. As
far as I can tell, the links and anchors are coded correctly.
But for some reason, I can't get the icons to be clickable.
The website is www.cleantelligent.com
Here's the code for the icons themselves:
<!--SOCIAL LINKS-->
<style>
#UpperLinks{ position: absolute; left: 50%; margin-left: 380px;
white-space: nowrap; padding-top: 27px;}
#UpperLinks img{ width:auto;}
#PhoneTop{ font-family: 'News Cycle', sans-serif; color:#D1D1D1; position:
absolute; left: 50%; margin-left: 345px; white-space: nowrap; margin-top:
-12px;}
</style>
<div id="PhoneTop">
<img style="position:relative; top: 8px;"
src="/wp-content/themes/cleantelligent/images/phonetrans.png" />(801)
375-0375</div>
<div id="UpperLinks">
<a href="http://www.linkedin.com/company/cleantelligent_software"
target="_blank" >
<img height="22" width="22"
src="/wp-content/themes/cleantelligent/images/linkedin.png" /></a>
<a href="https://twitter.com/#!/CleanTelligent1" target="_blank" >
<img height="22" width="22"
src="/wp-content/themes/cleantelligent/images/twitter.png" /></a>
<a href="http://www.facebook.com/CleanTelligent" target="_blank" >
<img height="22" width="22"
src="/wp-content/themes/cleantelligent/images/facebook.png" /></a>
<a href="https://www.youtube.com/CTsoftware" target="_blank" >
<img class="socialicons" height="22" width="22"
src="/wp-content/themes/cleantelligent/images/YouTubePlay.png" /></a>
</div>
<!--END OF SOCIAL LINKS-->