Translation:You cannot build houses in this zone.
The impersonal "si" is often used with an intended passive meaning, i.e. this sentence could be translated as "houses can't be built in this area"; in such cases the verb is conjugated accordingly with the intended subject (houses). It gets weirder if the sentence is formed by essere+predicate, because then the verb is to the singular and the predicate to the plural: "si deve essere buoni".
It would be "non posso" for "I cannot". This kind of construct (passive si) can only be used with a transitive verb and an intended subject in the third person, either singular or plural: http://www.zanichellibenvenuti.it/wordpress/?p=4024 is a very good reference for this, although all in Italian.
This all seems overly complicated for no valid reason. Wouldn't "Non si poter costruire case in questa zona" remove the confusion, especially if what is being conveyed is "you cannot" or "one cannot?" To introduce a plural conjugation of the verb into the sentence appears to be intentionally and, more important, unnecessarily obtuse. Am I wrong?
Sorry, I understand the stuff about it being impersonal and passive, but in English we use "You can't build"; "Houses can't be built"; "they can't build" pretty much interchangeably, but "they can't build" was marked as wrong. (we would rarely use the technically correct "one can't build")