If all that is impermanent is unsatisfactory, then is all that is permanent satisfactory? If all that has a beginning and an ending is impermanent and therefore unsatisfactory, then (with binary logic) that which has no beginning and no ending is permanent and satisfactory. 

Is this right or wrong? Why? And how does it change when applying catuskoti logic?
All 'things' are impermanent and unsatisfactory (and without self - these are the first three of the Four Dharma Seals). Your subsequent reasoning is wrong* and not Buddhist teaching either - Buddhism teaches neither nihilism nor permanence (one aspect of the Middle Way).

The point of the teaching of impermanence and unsatisfactoriness (and no-self) is to encourage you to give up your attachment to things as a source of happiness and security, and live within the fourth Dharma Seal, 'Nirvana is tranquility'.


Wrong in standard logic ('All Americans are mortal, therefore all non-Americans are immortal' - a fallacy known as 'denying the antecedent': https://en.wikipedia.org/wiki/Denying_the_antecedent ), and wrong with respect to the 'four possibilities', which are brought up in Madhyamaka philosophy simply for the purpose of being denied.