Why is $wpdb->get_results failing on certain tables but not others (which have data)?

you do not have to specify the $wpdb again in your query, but be sure that your table uses the prefix, if it has one. if it doesn’t, skip the part with the prefix.
also, you should always prepare a manually added query first.
this should do it:

global $wpdb;
$query = $wpdb->prepare( "SELECT * FROM %s", "{$wpdb->prefix}cart66_products" );
$rawproducts = $wpdb->get_results( $query );
print_r($rawproducts);