I don't think this is the easiest approach.
for a start, I'd use the ids as values instead of these additional hidden fields:
<?php
while ($x = mysql_fetch_row($dbaseQuery)
{
?>
<input type="checkbox" name="DeleteItem[]" value="<?php echo $x[0]; ?>">
<?php
}
then on your processing page, you can compose a comma-separated list of ids that were checked:
$id_list = implode(',', $_REQUEST['DeleteItem']); // or use $_POST or $_GET
and you'd need one query only, something like:
$sql = "DELETE FROM dbase WHERE LineID IN ($id_list)";
mysql_query($sql) or die (mysql_error());