It looks like the theme designer has a means for you to use a different logo on the homepage. Looking at your header.php on lines 83-93.
If your theme detects that this is the front page, the title is enclosed with an <h1> tag, otherwise it is enclosed in a <div>. Both have id='logo'.
If you can add custom css, you could use css image replacement to replace this <h1> tag with a different image on your homepage.