Without the HTML it's hard to say but you shouldn't have position: absolute and float: left on the same element - that doesn't really make sense.
You probably shouldn't be using position anywhere in your stylesheet for this.  It's usually something to stay away from unless you're scripting.
Edit: give this a go:
<style>
#greenback {
    width: 800px ;
    height: 250px ;
    background-color: #7EBB11 ;
    border: 3px solid #112D82 ;
}
#picright {
    float: right;
    display: block;
    margin: 11px 11px 11px 20px;
    width: 50%;
    height: 218px;
    border: 3px solid white;
}
#billboard  {
    width: 45% ;
    height: 99% ;
    border: 2px solid blue;
    float: right;
}
#billboard p {
    text-align: center;
    margin: 0;
    border: 1px solid red;
    margin-top: 50px;
    font-family: Optima, Calibri, Candara, Century-Gothic, Arial, sans-serif;
    font-size: 160% ;
    color: #ffffff ;
}
</style>
<div id="greenback">
    <img src="kids.jpg" alt="kids" id="picright" />
    <div id="billboard"><p>We help businesses,<br>communities and nature<br>take better care<br>of each other.</p></div>
</div>
                  Greg
                   2009-01-07 12:09:33