Kathleen
Still no precise place of birth for your TROJCAK ancestor?
I would think that the children's church baptismal record would provide you with parents place of birth.
This is the Austria-Hungary your ancestor came from
http://users.erols.com/mwhite28/austhung.htm where 12 different languages were spoken. What was language of your ancestors?
TROJC^AKs in Slovakia's phone book:
http://www.zoznam.sk/hladaj.fcgi?co=telzoznam&s=trojcak&...KOSTKAS^ in Slovakia:
http://www.zoznam.sk/hladaj.fcgi?co=telzoznam&s=kostkas&...Have you looked in NY Ellis Island site at TROJCSAKs, TROJCAKs, KOSTKAS manifest? Family went to family in the beginning. Possible someone arriving NY EI went to the address of your ancestor.