1-They didn't pay me(what=anything) except for one month.
2-They didn't pay me but for one month.
3-Except for one month they didn't pay me.
4-But for one month They didn't pay me.
Except for and but for are standard idiomatic expressions: meaning if it were not for/ were it not for. But basically they are prepositional phrases and can be used at the beginning or end of the sentence. So there is nothing wrong with construction of all the sentences. But the prepositional phrase should complement the direct object a noun or pronoun (in place what) which can be salary, emoluments or anything, so as to give sense to the sentences. To be more specific it could be said: They didn't pay me anything except for one month’s salary.