If the divs are hidden, they will never trigger the mouseover
event.
You will have to listen to the event of some other unhidden element.
You can consider wrapping your hidden divs into container divs that remain visible, and then act on the mouseover
event of these containers.
<div style="width: 80px; height: 20px; background-color: red;"
onmouseover="document.getElementById('div1').style.display = 'block';">
<div id="div1" style="display: none;">Text</div>
</div>
You could also listen for the mouseout
event if you want the div to disappear when the mouse leaves the container div:
onmouseout="document.getElementById('div1').style.display = 'none';"