Horizontal Social Media Icon

I know this topic has been covered, but everything I’ve tried so far based on the answers in previous threads is not working.

I have added two social media icons to the top right of my header on my site, http://www.burlingtonbookfestival.com (using a child theme of twenty-eleven). I have been trying to get the two icons to line up horizontally, but no matter what I try to do, they stay lined up vertically. I know very little about .php, so I don’t know if the problem is there (although I doubt it, I’m pretty sure it’s a CSS issue I’m just missing). I’m pretty good with CSS, and this is what I have right now:

#header_icons {
float: right;
width: 100px;
margin-top: 5px;
}

#header_icons ul {
height: 50px;
width: 50px;
}

#header_icons ul li {
display: inline;
float: left;
height: 50px;
margin: 0px;
padding: 0px;
}

#header_icons li{
display: inline;
}

#header_icons img {
margin: 0px;
padding-left: 15px;
width: 50px;

I’ve tried fixing the problem in Firebug, but no matter what I try (including changing the right float to left on #header_icons), it’s still not fixing the issue. Any help would be greatly appreciated!