My great-great-grandfather's name was William McHale. He could have been a brother to your Michael. We don't know his birthplace beyond Mayo and believe that he married Mary Rogan in Mayo before coming to Carbondale very early (possible 1847) He seems to have been in the earliest possible wave of famine immigrants but we don't know his exact arrival. His children included an Edward (although I don't recall a Michael (who might have been named after a brother if he had one.) He lived to 1898.
We also had another McHale line whose father was Michael. He MAY have been married to a woman named Sarah Battle Tighe McHale, who had been widowed twice before marrying Michael. Their daughter was Bridget McHale who married my great grandfather on another side - Martin Fortune. Do any of these names ring any bells.