I understand your frustration at not finding earlier records. I can find no immigration record for Anna Gegan that matches the birthdate and approximate arrival dates that I have for her.
I have, however, found an 1860 census record that could be for your Patrick Gagen. He has been indexed as "Pateric Gaggen" with a birthdate of 1835 and is shown living in Pine Township, Armstrong County, Pennsylvania with a James Gaggen and next door to a Chris Gagen and his family.
Hopefully you can find this via an Ancestry search. But if not let me know and I can mail it to you.