Links Vanish, Can't Figure This Out! Going Crazy!

Ok, so I am using xammp, have WordPress installed on a localhost and am set up in Dreamweaver and everything is going peachy except for this: I have styled my posts to have the appearance of a mp3 player and have it set up so that I only have to add a bit of code to a post in text mode and everything looks real slick. Inside that (which is mostly shortcodes) is:

<div class="downloadbuyWrapper">

<div class="buynowBtn"><a href="LINKS TO WP PAGE"><img src="IMAGE SOURCE" /></a></div>

<div class="downloaddemoBtn"><a href="DOWNLOAD LINK"><img src="IMAGE SOURCE"/></a></div>
</div>

I then have said div classes defined and nicely styled in dreamweaver and everything looks perfect. BUT when the page is previewed in Chrome the link images disappear WHEN CLICKED and nothing happens. In Firefox they flash when clicked and still nothing. In IE it works?!?! First time I’ve ever had IE work the way it should when other browsers don’t!
This is getting really frustrating for me, and I can’t seem to figure it out or find any info online about it! Any help would be greatly appreciated!