Q:

How to retrieve all recursive children of parent row in Oracle SQL?

I've got a recursive query that's really stretching the limits of this Java monkey's SQL knowledge.  Now that it's finally 1:30 in the AM, it's probably time to start looking for some help.  This is one of the few times Google has failed me.
The table is as follows:
Parent_ID CHILD_ID QTY
25        26        1
25        27        2
26        28        1
26        29        1
26        30        2
27        31        1
27        32        1
27        33        2

I'm trying to get the following result, where the parent has every child listed below them.  Note that the qty's cascade as well.
BASE    PARENT_ID  CHILD_ID   QTY
25         25        26        1
25         25        27        2
25         26        28        1
25         26        29        1
25         26        30        1
25         27        31        2
25         27        32        2
25         27        33        4
26         26        28        1
26         26        29        1
26         26        30        2
27         27        31        1
27         27        32        1
27         27        33        2

I've tried several deviations of the following to no avail.
SELECT *
FROM MD_BOMS
START WITH PARENT_ID is not null
CONNECT BY PRIOR CHILD_ID = PARENT_ID
ORDER BY PARENT_ID, CHILD_ID

I'm using the Oracle database.  Any suggestions, ideas, etc. would be greatly appreciated.  This seems close, but I'm not sure if it's what I'm looking for: Retrieve all Children and their Children, recursive SQL
Based on ( Retrieve all Children and their Children, recursive SQL )I've also tried the following but receive an "illegal reference ofa  query name in WITH clause" error:
with cte as (
    select  CHILD_ID, PARENT_ID, CHILD_ID as head
    from    MD_BOMS
    where   PARENT_ID is not null
    union all
    select  ch.CHILD_ID, ch.PARENT_ID, p.head
    from    MD_BOMS ch
    join    cte pa
    on      pa.CHILD_ID = ch.PARENT_ID
)
select  *
from    cte

A:

You are close:
select connect_by_root parent_id base, parent_id, child_id, qty
from md_boms
connect by prior child_id = parent_id
order by base, parent_id, child_id;

          BASE  PARENT_ID   CHILD_ID        QTY
    ---------- ---------- ---------- ----------
            25         25         26          1 
            25         25         27          2 
            25         26         28          1 
            25         26         29          1 
            25         26         30          2 
            25         27         31          1 
            25         27         32          1 
            25         27         33          2 
            26         26         28          1 
            26         26         29          1 
            26         26         30          2 
            27         27         31          1 
            27         27         32          1 
            27         27         33          2 

     14 rows selected 

The connect_by_root operator gives you the base parent_id.
SQL Fiddle.
I'm not sure how you're calculating your qty. I'm guessing you want the total for the path to the child, but that doesn't match what you've shown. As a starting point, then, borrowing very heavily from this answer, you could try something like:
with hierarchy as (
  select connect_by_root parent_id base, parent_id, child_id, qty,
    sys_connect_by_path(child_id, '/') as path
  from md_boms
  connect by prior child_id = parent_id
)
select h.base, h.parent_id, h.child_id, sum(e.qty)
from hierarchy h
join hierarchy e on h.path like e.path ||'%'
group by h.base, h.parent_id, h.child_id
order by h.base, h.parent_id, h.child_id;

     BASE  PARENT_ID   CHILD_ID SUM(E.QTY)
---------- ---------- ---------- ----------
        25         25         26          1 
        25         25         27          2 
        25         26         28          2 
        25         26         29          2 
        25         26         30          3 
        25         27         31          3 
        25         27         32          3 
        25         27         33          4 
        26         26         28          1 
        26         26         29          1 
        26         26         30          2 
        27         27         31          1 
        27         27         32          1 
        27         27         33          2 

 14 rows selected 

A:

@AlexPoole answer is great, I just want to extend his answer with more intuitive variant of query for summing values along a path.
This variant based on  recursive subquery factoring feature, introduced in Oracle 11g R2.
with recursion_view(base, parent_id, child_id, qty) as (
   -- first step, get rows to start with
   select 
     parent_id base, 
     parent_id, 
     child_id, 
     qty
  from 
    md_boms

  union all

  -- subsequent steps
  select
    -- retain base value from previous level
    previous_level.base,
    -- get information from current level
    current_level.parent_id,
    current_level.child_id,
    -- accumulate sum 
    (previous_level.qty + current_level.qty) as qty 
  from
    recursion_view previous_level,
    md_boms        current_level
  where
    current_level.parent_id = previous_level.child_id

)
select 
  base, parent_id, child_id, qty
from 
  recursion_view
order by 
  base, parent_id, child_id

SQLFiddle example (extended with one data row to demonstrate work with more then 2 levels)

