How is rebirth to be understood? I have some questions regarding this Buddhadhasa text saying there is no rebirth in Buddhism. 
Is rebirth not what enlightenment is supposed to bring an end to? Is there no rebirth because rebirth is actually to be understood in a moment-to-moment manner unrelated to the end of life (rebirth as pertaining to the condition of willing no more)? Then why does Goenkaji talk about "good fortune from a past life"? I thought I also heard him imply the rebirth of our consciousness in the context of suicide being a bad idea for this reason.
Buddhadhasa text saying there is no rebirth in Buddhism


The Buddhadasa text states 'birth' is the mental birth of the 'self' or 'I' thought and that there is no 'rebirth' because each time the conditioned 'I' thought is born it is a brand new 'I' rather than the same 'I' being reborn. 

For example, is the 'I' you sense yourself to be today the same 'I' as when you were 4 years old? 

Buddhadasa concluded there is on-going 'ego-birth' for unenlightened people but not 'rebirth'.


  Is rebirth not what enlightenment is supposed to bring an end to?


The Pali scriptures state enlightenment brings about the end of the "I-conceit" (MN 22); the end of 'I-making' &amp; 'my-making'. 

The Pali scriptures (very end of MN 38) states 'birth' ends while the mind remains conscious, which supports Buddhadasa's view that 'birth' refers to the birth of the 'I' concept. 

SN 22.81 also supports Buddhadasa's view. 


  Is there no rebirth because rebirth is actually to be understood in a moment-to-moment manner unrelated to the end of life (rebirth as
  pertaining to the condition of willing no more)?


According to Buddhadasa, yes. 


  Then why does Goenkaji talk about "good fortune from a past life"?


This is a common idea in cultural Buddhism &amp; Hinduism, which also probably explains why Buddhism became extinct in India (since both doctrines became essentially the same). 


  I thought I also heard him imply the rebirth of our consciousness in the context of suicide being a bad idea for this reason.


Yes, this is also a common idea and possibly a beneficial idea, namely, to discourage people from committing suicide. However, there are no references in the Pali suttas I have read where the Buddha was pre-occupied with this concern. 

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The following discussion supports Buddhadasa's viewpoint:

DN 15 is the only discourse from thousands attributed to the Buddha, I am aware of, which makes an unclear inference that consciousness is 'reborn' (i.e., enters into a mother's belly).

Why DN 15 is unclear &amp; considered by many scholars, including scholars that believe in reincarnation/rebirth, to be unauthentic is because it contradicts the many other reported discourses on the same subject.

In the many other discourses, such as MN 43, SN 22.79, MN 9, MN 148, MN 18, SN 12.2, SN 12.67, SN 22.56, SN 22.82, MN 38, SN 22.53, etc, it is written that: 


consciousness is (only) mental cognition (MN 43, SN 22.79); 
there are only six types of consciousness (SN 12.2; MN 9; MN 148);
consciousness arises in dependence on sense organs &amp; sense objects (MN 148, MN 18, MN 38);
consciousness is caused by the mind-body (SN 12.67, SN 22.56, SN 22.82);
for consciousness to arise without the body, feelings, perceptions &amp; mental formations is impossible (MN 38; SN 22.53). 


In summary, similar to DN 15, the idea the consciousness is reborn in the form of a 're-linking consciousness', 'stream of consciousness', 'mindstream', 'storehouse consciousness', etc, are all ideas created after the passing of the Buddha by different &amp; various Buddhist schools. These terms about a 'rebirth consciousness' commonly used by Buddhists have no source in the original teachings. 

The Pali scriptures actually state that "beings" ("sattā") or "men &amp; women " (itthī vā puriso vā) are 'reborn'. To quote:


  When the mind was thus concentrated, purified, bright, unblemished, rid of defilement, pliant, malleable, steady, &amp; attained to
  imperturbability, I directed it to the knowledge of the passing away
  [fall] &amp; reappearance [rise] of beings (satta).
  
  Here, student, some woman or man is a killer of living beings, murderous, bloody-handed, given to blows and violence, merciless to
  living beings. Due to having performed and completed such kammas, on
  the dissolution of the body, after death, he/she reappears in a state of
  deprivation, in an unhappy destination, in perdition, in hell.


In SN 5.10 &amp; SN 23.2, a "satta" ('being') is described as a 'view' ('idea') about the totality of the five aggregates born from attachment &amp; craving. To quote:


  Why now do you assume 'a being'? Mara, have you grasped a view? This is a heap of sheer constructions: Here no being is found.
  
  Just as, with an assemblage of parts, The word 'chariot' is used, So, when the aggregates are present, There's the convention 'a being'.
  
  SN 5.10
  
  'A being,' lord. 'A being,' it's said. To what extent is one said to be 'a being'?"
  
  Any desire, passion, delight, or craving for form, feeling, perception, mental formations &amp;/or consciousness, Radha: when one is
  caught up there, tied up there, one is said to be 'a being.'
  
  SN 23.2


Therefore, based on the words attributed to the Buddha, what is 'reborn' appears more likely to be the 'self-view' or 'I-thought' based on all of the five aggregates rather than only consciousness being 'reborn'. In MN 38, the Buddha is reported to have heavily criticized &amp; admonished a monk for holding the view that consciousness is reborn. To quote:


  As I understand the Dhamma taught by the Blessed One, it is just this consciousness that runs and wanders on, not another.
  
  Which consciousness, Sāti, is that?
  
  This speaker, this knower, lord, that is sensitive here &amp; there to the ripening of good &amp; evil actions.
  
  And to whom, worthless man, do you understand me to have taught the Dhamma like that? Haven't I, in many ways, said of dependently
  co-arisen consciousness, 'Apart from a requisite condition, there is
  no coming-into-play of consciousness'? But you, through your own poor
  grasp, not only slander us but also dig yourself up [by the root] and
  produce much demerit for yourself. That will lead to your long-term
  harm &amp; suffering.


In conclusion, the ideas of people such as Goenka, which are also held by the majority of Buddhists, seem to have next to no basis in the original Pali scriptures. Where as the ideas of Buddhadasa at least seem to conform with a diligent (rather than superficial) examination of the original Pali scriptures. Further, the ideas of Buddhadasa can also be verified by meditative insight (where as the ideas of Goenka cannot), which conforms again with MN 38, which states: 


  Good, monks. You have been guided by me in this Dhamma which is to be seen here &amp; now, timeless, inviting verification, pertinent, to be
  realized by the observant for themselves.