I've not been able to find any kind of birth record for this David Williams. On the 1851, 1861, 1871 census he claims to have been born in Llansaintffraid, Montgomeryshire. He married Elizabeth (maiden name probably "Randles") around 1832, though I see no record for a marriage either. They lived in the area (including Carreghofa.)
I've tried Ancestry.com and other sites. No luck.
Any idea where to look?