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After ordination Father Parkes served as the parochial vicar of Holy Family Parish in Orlando, Florida (1999–2005) and he was the founding pastor of Corpus Christi Parish in Celebration, Florida from 2005–2012.
After ordination Father Cary served as the parochial vicar at St. Joseph Parish in Salem, Oregon (1992–1995), archdiocesan vocation director (1995–1999) and pastor at Sacred Heart Parish Medford, Oregon, St. Luke's in Woodburn, Oregon (1999–2011) and St. Mary's Church in Eugene, Oregon (2011–2012).
Serving the Archdiocese of Cochabamba he was parochial vicar in Sacaba and Villa Tunari, and then parish priest in Condebamba of Cochabamba (from 1996 to 2000).
From 1974 to 1988 he taught religion and was parochial vicar in the parishes of Santhià and Moncrivello.
Later he held the following pastoral assignments: Parochial Vicar at St. Anne at Radcliffe on Trent (1987–1988), Professor of Moral Theology at All Hallows College (1990–98), Professor of Moral Theology and Director of Studies at the inter-diocesan seminary in Wonersh (1998–2004), Parish Priest of Our Lady of Lourdes, Mickleover, Derbyshire (2004–09).
After completing his seminary studies in the American College of Louvain (Leuven), he was ordained to the presbyterate for the diocese of Honolulu at Saint John Vianney Church in Kailua on October 18, 1985 where he served as a parochial vicar.
After Ordination, he served in various positions: Parochial Vicar, Pastor, Prefect, and Professor in the Major Seminary and Minor Seminary, Judge and Promoter of Justice in the Diocesan Tribunal, and ultimately as Episcopal Vicar of the Vicariate of Texcoco in the Texcoco Diocese.