The IGI has an entry for JAMES WILLIAM STARKIE Christening: 12 JUN 1864 Cathedral, Manchester, Lancashire, England, Father: JAMES STARKIE, Mother: MARGARET.

I assume you got his parents' names from his marriage cert? What exactly does his NZ death cert have for his place of birth and how long in NZ? Also for his father's occupation?

The 1871 Ancestry census has Grandsons James Starkey aged 7 and William Starkey aged 4 living with their LEWIN grandparents in Marown, who I think are more likely to be your relatives than the Lancs bapt, above, unless the b."Braddan" is an error:
Household Members: Name Age
Charles Lewin 60 Ag lab b.Braddan
Isabella Lewin 61 wife b.Braddan
Eleanor Lewin 29 daur Serv Genl b.Marown
John Lewin 24 son Ag Lab b.Braddan
James Starkey 7 grandson scholar b.Braddan
Jane Lewin 14 granddaur scholar b.Braddan
William Starkey 4 grandson scholar b.Braddan

In the 1881 census (also on Familysearch.org) James is a servant in another family and William is with an uncle:
Jacob LEWIN Head M Male 29 Isle of Man, England Lead Miner
Ann LEWIN Wife M Female 27 Isle of Man, England
Jacob LEWIN Son Male 3 Isle of Man, England
Ann LEWIN Daur Female 1 Isle of Man, England
William STARKEY Nefew Male 15 Isle of Man, England ((Farm)) (Ag) Lab
Source Information:
Dwelling 3 Stagadhoo
Census Place Marown, Isle of Man, Isle of Man
Family History Library Film 1342344
Public Records Office Reference RG11
Piece / Folio 5597 / 112
Page Number 12

The IGI also has an entry for JAMES STARKEY & MARGARET LEWIN Marriage: 11 NOV 1863 Malew, Isle Of Man, but you need the information from the NZ certs first to be certain that you have the right ancestry for your William.

Sue