You are sort of the right track regarding Ruth. She was not born in the colonies but in Dennington, Suffolkshire, England, about 1632. She emmigrated from England to Massachusetts with her parents in 1637.
Her youngest sister, Sarah, was the last child of Austin and Alice Kilham, born in Dedham, Massachusetts, January 4, 1641/42. Ruth married a fellow named William McKinney in Dedham, Massachusetts. The resources you are looking for are the Vital Records of Dedham, Mass. throught 1850; The Dedham Town Records, and the Dedham Church Records. There are several other resources for Dedham which you can buy through the Dedham Historical Society (chech web for their site). I have all these original books in my personal library.
The Kilham/Killam family society last met just before WW II in Boxford, MA. People lost interest after that time period. I am probably ther best living resource for colonial Kilhams and as such I am willing to help you in any way I can. E-mail me directly at firstname.lastname@example.org. I live in Connecticut now, originally from Massachusetts. Where do you live?