If you want to analyze "satisfaction" as a non-simple form, the etymology-based way of doing it would be satisfy + the nominalizing suffix -(t)ion, with a contextual change of satisfy to an allomorph "satisfac-" in this context. (I wrote -(t)ion because it's not entirely clear whether the "t" should be interpreted as part of the suffix; it also shows up in words with other endings like satisfactory.)
The Latin source of satisfy had a C in the stem; sound changes caused this to be lost in French (the proximate source of the word satisfy), but it shows up in the related noun. The noun "action" is unrelated. We see a similar phenomenon of English verbs and related -tion nouns having different "stems" with e.g. destroy, destruction or conceive, conception.
If you don't like using etymology as a criterion for the present-day morphological structure of English words, you could just analyze "satisfaction" as a "portmanteau morph" for the morpheme satisfy + whatever nominalizing morpheme is present in abstract nouns that end in -tion. The concept of a "portmanteau morph" is that you don't have to identify which part of the form corresponds to which morpheme (unit of meaning); rather, you just say that the combination of the two morphemes corresponds to some unitary form (in this case, "satisfaction").
I'm not sure whether dis- should be analyzed as attaching to the verb (forming dissatisfy, which is then nominalized) or the noun satisfaction in this context.