In the sentence:
Non debes officia deorum desiderare
officia could be accusative or nominative plural. I was thinking it was accusative as officia is what ought not to be desired (debes is working on officia). If that is the case then what is the subject since nothing else is in the nominative?
Debeo is what is known as a prolative verb. As in English a large number of verbs can be followed by the infinitive - “he tried to help”, “I wanted to go”, “I ought to finish this”. In that last one I is of course in the nominative, and this is the subject.
Verbs that can be followed by the infinitive include:
(a) those to do with (in)ability, for example - possum, queo, nequeo
(b) those to do with wish, intention, effort, for example - volo, malo, opto, statuo, conor, audeo, tempto
(c) (as here) obligation or habit - debeo, soleo
(d) begining and ending (in english we would follow this with a gerund - e.g. stop dancing) - desino, incipio, desisto
(e) knowing, teaching and learning. In English we’d say “he learnt how to swim”, “we taught him how to whistle”, or “she knew how to sing”. Latin just uses the infinitive: Vincere scis, victoria uti nescis - You know how to win, you do not know (not know = nescis) how to use victory (utor/uti takes an ablative object)
HTH
The subject of the entire sentence is implied by debes - you. But it is really enough to know that desiderare is an objective infinitive and officia is its direct object
As stated by Deses, due to the conjugation of verbs, no subject is required. As a matter of fact, if the verb is in the first or second person you usually will not have a subject.