Display broken when moving from php 5.2

I’ve used this theme on this site for ages and really like it. However, I’ve not been able to upgrade my php version from 5.2 because the site doesn’t look right with 5.3-5.5.

Here’s how it’s supposed to look:

Here’s what it looks like using php 5.3-5.5:

I upgraded the theme to the latest version from the WordPress dashboard, but the newest version of Esplanade still shows incorrectly with php 5.3-5.

Any ideas on what this is and how to remedy it?

Thanks