Did you look at BANASCHEK, BANASZAK in Ellis Island. It is possible that your ancestor made a mistake on the year, ship name or port of arrival.
I suspect that he might have used Lomza but that most likely was not his place of birth.http://www.szczuczyn.com/maplomzagub.htmhttp://genforum.genealogy.com/cgi-bin/search.cgi?forum=polan...
You might want to post a query on Poland's Ancestry board.
You looked already at these EI arrivals?
Banaschak, Jan Jonne, Russia 38 1871 1909
Banaschek, Jan Brudki, Russia 21 1886 1907
Banaschek, Jan Budy 19 1887 1906
Banaszak, Jan Skulsk, Russia 20 1893 1913
Banaszak, Jan Swiencien, Kalisch, Russia 28 1882 1910
Banaszak, Jan Russia 19 1891 1910
Banaszek, Jan Slotkaw, Russia 23 1890 1913