In the button click call the javascript to display the div as:
string script = "<script language='javascript'>visiblediv()</script>";
ScriptManager.RegisterStartupScript(Page, Page.GetType(), Guid.NewGuid().ToString(), script, false);
and for closing call the closing function somewhere at the appropriate palce, for this i will suggest to place a closing link in the div only such as :
<a href="#"><img src="../images/close_icon.gif" alt="Close" width="14" height="14" border="0"
önclick="invisiblediv()" style="cursor: pointer;" /></a>