Here's one approach. This approach does not require an inline view (derived table), and can be effective if you want to include flags for multiple conditions:
EDIT:
This returns custID
that has a row for all four items:
SELECT t.custID
, MAX(IF(t.orderComponent='breadsticks',1,0))
+ MAX(IF(t.orderComponent='pizza',1,0))
+ MAX(IF(t.orderComponent='salad',1,0))
+ MAX(IF(t.orderComponent='wings',1,0)) AS has_all_four
FROM mytable t
GROUP BY t.custID
HAVING has_all_four = 4
ORIGINAL ANSWER:
(This checked for a customer "order" that had all four items, rather than just a "custID".)
SELECT t.custID
, t.orderID
, MAX(IF(t.orderComponent='breadsticks',1,0))
+ MAX(IF(t.orderComponent='pizza',1,0))
+ MAX(IF(t.orderComponent='salad',1,0))
+ MAX(IF(t.orderComponent='wings',1,0)) AS has_all_four
-- , MAX(IF(t.orderComponent='breadsticks',1,0)) AS has_breadsticks
-- , MAX(IF(t.orderComponent='pizza',1,0)) AS has_pizza
-- , MAX(IF(t.orderComponent='salad',1,0)) AS has_salad
-- , MAX(IF(t.orderComponent='wings',1,0)) AS has_wings
FROM mytable t
GROUP BY t.custID, t.orderID
HAVING has_all_four = 4
That will get the "orders" that have all four items. If you want to return just values for custID, then use the query above as an inline view (wrap it in another query)
SELECT s.custID
FROM (
SELECT t.custID
, t.orderID
, MAX(IF(t.orderComponent='breadsticks',1,0))
+ MAX(IF(t.orderComponent='pizza',1,0))
+ MAX(IF(t.orderComponent='salad',1,0))
+ MAX(IF(t.orderComponent='wings',1,0)) AS has_all_four
FROM mytable t
GROUP BY t.custID, t.orderID
HAVING has_all_four = 4
) s
GROUP BY s.custID