Add some or die's for error checking:
<?php
$db = mysql_connect("localhost","chad1_chad","iruleu") or die(mysql_error());
mysql_select_db("chad1_test",$db) or die(mysql_error());
$query = mysql_query("SELECT * FROM APX_members") or die(mysql_error());
while($row = mysql_fetch_array($query)){
echo "<td>".$row[last_name].", ".$row[first_name]."</td>";
}
?>
Let's see if the query or select are failing... because ShawnK's code should have worked... Are you sure you are putting the right username/host/password, etc? Also, the table and DB names are case sensitive, so double-check that...