You're welcome. Yes it's decomposed as you explained.
Hatırla (root) + (y)a (negative ability/possiblity) + maz (negative aorist) + dı (past) + m (first person)
Hatırlardım -> I would have remembered
Hatırlamazdım - I would not have remembered
Hatırlayamazdım - I would not have been able to remembered or I could not have remembered
Google translate says:
hatırlayamadım = I cannot remember
hatırlayamazdım = I could not remember
I must admit I am not sure at all, tips and notes gives for
I cannot remember : hatırlayamam (this is my own creation ;-) and it is how I understand the way creating such a verb)
So I am a bit confused about this topic and would appreciate if any native speaker or anyway knowing person would give us a helping hand.
I've noticed that hatırlayamadım and hatırlayamazdım are often (semantically) used interchangeably when translating to English.
Having said that, however, I will still attempt to clarify the subtle difference.
hatırlayamadım (I could not remember) Eg. "Adresi hatırlayamadım" ("I couldn't remember the address").
hatırlayamazdım (I could not have remembered) Eg. "Eğer bir yere yazmamış olsaydım, adresi hatırlayamazdım" ("If I hadn't written it down somewhere, I couldn't have remembered the address).
hatırlamazdım (I would not have remembered)