Venn suggests:
Matric. sizar from MAGDALENE, Easter, 1636; B.A. 1639-40; M.A. 1643. Perhaps ord. priest (Lincoln) Mar. 17, 1643-4. One of these names (M.A.), V. of Sutton, Cambs., 1663-76. Buried there Oct. 9, 1676. [No other John Marshall in Venn fits so well]