Both of my great-great grandparents were Jews who came to America. Their son, my great grandfather was a Jew who married an Irish woman. (I do not know if she went through conversion.) Together they had my grandmother, who married a native American and had my mother. Does this mean that I am Jewish?
Judaism is defined by the maternal line. Your maternal grandmother was non Jewish since her mother was Irish, and same therefore goes for you. There are worse things in life:)