Thanks for the input guys. I tried my hand at it and frankly, I'm surprised I got anything to work as intended. I have a carousel that displays manufacturer, series and product information and I stared it down logically (pffft) and came up with this, which works:
$result = mysql_query("
products.prod_image IS NOT NULL
products.prod_series = series.series_id
series.series_man = manufacturers.man_id
") or die(mysql_error());
How ultra-inefficient is that? haha