The Patrick & Mary listed in Dedham could not have been William's parents. Their children were born in Dedham in the 1850's.
Patrick was naturalized on Oct 23, 1872, USCC Boston, MA, cert # 62-130. He was born March 1850 in Ireland.
Have you ordered the naturalization records? It may give you a port of arrival. You can do so online at http://www.archives.gov/research/order/
I believe it cost $7.50, well worth the cost. I have gotten a lot of valuable info from these documents.