The parish registers (in common with the registers of all parishes in the diocese of Derbyshire) are at the Derbyshire Record Office in Matlock. They offer a paid research service.
The chances of finding any mention of a father on an 1834 marriage register entry are extremely slender - the only occasions on which I have seen it have been when one of the parties is a son or daughter of the incumbent. The original entry will, however, show the names of two witnesses. who may be family members and offer a clue. The register will also tell you if either party was widowed and their parish of residence (not birth).
Caroline