Thanks for your message. I hope that someone with information makes a connection with you and helps you to further your research.
In the meantime, did you know that church records from Dublin have been uploaded to http://churchrecords.irishgenealogy.ie/churchrecords/
Perhaps if you can find Edward?s baptism record here it will give you his parents names.
Have you tried looking into the family?s emigration? Sometimes more infomation can be found at the port of arrival rather than that of departure. For information on US immigration records check http://www.archives.gov/research/immigration/
Some other websites that may be useful are:
The National Archives of Ireland http://www.nationalarchives.ie/genealogy1/genealogy-records/introduction/
The National Library of Ireland http://www.nli.ie/en/family-history-introduction.aspx
Irish Genealogy Tool kit: http://www.irish-genealogy-toolkit.com/
Genealogy Links: http://www.genealogylinks.net/uk/ireland/dublin/index.html
Dublin Heritage: www.dublinheritage.ie