Andrew

Might the surname be BARNA and not Barno and PLIS'KA and not Plisca?
The SK's phone site www.zoznamst.sk is listing PLIS'KA and BARNA.

When your ancestors were born it was Austria-Hungary empire : http://users.erols.com/mwhite28/austhung.htm
The country of Czechoslovakia in 1993 separated into Czech Republic and Slovak Republic.
I would take a guess and suggest a research in Slovak Republic. The LDS-Mormons have filmed the church records but you need the name of a town and a religious orientation of your ancestor to order the films.
www.bmi.net/jjaso to familiarize yourself with church wording.
www.iabsi.com/gen/public
www.slovaklinks.com
www.slovakfolkcrafts.com
www.our-slovakia.com
www.village.sk
www.slovakinstitute.com
www.tccweb.org
www.c-rs.org
www.adc.sk/english/slovakia/slovak04.htm