Venardos Family History

Hello,

I am a young historian trying to find records of my great-great grandfather John Peter Venardos parents. He was born on October 10, 1872 in Kythera, Greece and immigrated through Ellis Island, NY around 1901-1902? Some years later, he and his brother were owner/operators of Venardos Candy Kitchen and Ice Cream Parlour, with three locations in Alton, IL. He was married to Edith "Eda" Hack and had four children, in age order, named Elizabeth "Liz" Venardos, Nestor John Venardos, Dia Venardos, and Homer Frederick Venardos. My grandpa, Lane Beall Venardos, is his grandson (1944-2011), and his son Kevin Venardos, found John Peter Venardos on the Wall of Honor for immigrants. The other guy, possibly a brother, was named Peter Michael Venardos. He died on October 3rd, 1968 in Alton, IL. On Ancestry, it says that his dad might have been named Peter Benardos, born in Swiss Alps, but there is no lead and no records, with no mother also. If someone could please help me, that would be great.