It's probably because you're using AND instead of OR - it's not often that a property is going to be in E8 AND N19, is it?
AND paddress1 like\"%$stname%\" AND
(ppostcode like\"$area1%\" OR ppostcode like\"$area2%\"
OR ppostcode like\"$area3%\" OR ppostcode like\"$area4%\"
...etc. )
AND pg1=1
etc.
But I don't think you'll be happy with the results. ppostcode like "%" is not a smart thing to have.
You don't need to put the entire query together at once.
$query_PD = "SELECT * FROM property WHERE pavailable='1' AND synchDel !='1'
AND paddress1 like\"%$stname%\" ";
$areas = array();
if(isset($area1)) $areas[]="ppostcode like \"$area1\"";
...
$areas = join(' OR ', $areas);
if($areas!='')
{
$query_PD .= " AND ($areas)";
}
$query_PD .= " AND pg=1....";
(PS: they're checkboxes; radio buttons are different.)