Oh good, so at least we're on the right track

I'm having difficulty in finding the Dodds in earlier censuses; there are other Dodds in the area, possibly related to your ones. It's not a very common name for Breconshire in those times.
There's a possible 1841 entry, which could be John's father William with his own parents:
1841 HO107 1370 8 7 6 and 7
Tynanin? North Gwenddwr
William DODD 65 Farmer, looks like N in "Whether born in same county"
Margaret Wife 45 Y
William Son 20 no occupation stated Y
So perhaps this William Dodd came from Ireland?
Possible marriage for William and Ann, John's parents:
Sep Qtr 1846 Builth Vol 26 Page 419
William DODD
Ann WILLIAMS
Glad to hear your cousin is still around; it's amazing what info they can come up with. And I would recommend getting some later birth and/or marriage certificates so that you can confirm or discount the census info that we've found.
Kind regards
Gaie