If no files are attached to a page, the files module reports "No files attached to this page." However that text is difficult to style using CSS. It requires an external div and then child selectors, eg div.mydiv>div>p:first-child The <p> should have a CSS class (it has to be a class because there can be more than one of these on the page.)
The HTML generated by the files module looks like this:
<div id="files-927607"> <p> No files attached to this page. </p> <script type="text/javascript"> ...</script> <p class="manage-attachments-link" style="text-align: center;"> ... </p> </div>