Today there are appx 20,000 Demchuk/Demczuk = Демчук living in Ukraine. It is a very common surname!
The only possible connection your Demchuk might have w/this Demchuk from Dniepropetrovsk is there were Cossack in the 16th century, who came West to the aid of the Polish King against the Ottoman hoards. Some decided to stay after that and settled in the Carpathian general area and some went home, to Central Ukraine.
GGGrandparents Petro and Nastasia (Anastazia) DEMCZUK (pronounced just like Demchuk) arrived in Halifax, Canada w/their children in April 1899 on the SS Palatia.*** They were emigrating from Szubranetz >Austria. This was in the Historic Bukowyna Province, the Land of Beech Trees. Today the village is called Shubranetz = Шубранець in Ukrainian > Zastavnivskiy raion/district > Chernivetska (Chernivtsi) oblast/region. The village recently celebrated its 574th anniversary, although there was settlement there, dated scientifically back to 5500BC. It was called the Trypillian Culture. 5500BC is PRE Egyptian Pharoah Period.
Pradeedo and Prababa were likely Christian Orthodox and those church registers for your ancestral village have been filmed by LDS. The difficulty is reading the records, as it is in Old Church Slovanic. https://familysearch.org/search/catalog/1336919?availability...http://familysearch.org/learn/wiki/en/Bukovina_Church_Record...
Post your inquiry in the Chernivetskij sub-forum and you will find some very knowledgeable researchers there to help you research your Bukowynian Heritage.
***Hamburg Passenger Records - It is the second Petro listed.http://search.ancestry.com/cgi-bin/sse.dll?db=HamburgPL_full...