Births weren't recorded in Virginia until about 1856 so that option is out.
I looked at the records at the Library of Virginia, www.lva.virginia.gov/public/local/results_all.asp?CountyID
but didn't see any labeled Adoption. However there should be Guardian records before the Adoption records. You'll probably have to ask the Virginia Library.
After you've identified the film you want to view, contact your local, public library and ask them to obtain the film via inter-library loan.
I'd also contact the Albemarle Charlottesville Historical Society, http://albemarlehistory.org//index.php/library
and ask if they have any of those records.
Your next option is DNA testing. Successful Searching!