DNA testing is not straightforward. There are three different tests you can take, each of which is used differently.
Autosomal DNA tests are really only useful for the last 6 generations or so, because the ancestors' genes get watered down. But autosomal does indicate what sort of relationship there could be and how distant it is.
YDNA is only for chaps; ladies can get their father or brother to take it for them if they are sure the chap really is their father or brother. YDNA traces the direct male line going back quite some time, and if that someone you are tracing is a chap, he might have the same YDNA as you ... if you are a chap.
Everyone has mtDNA, but it is only passed by women. A direct female line can be traced back many generations, and a total stranger can match your mtDNA exactly, showing that you have a common female ancestor. The modern full sequence mtDNA is far more reliable than the older HVR1 and 2 tests, but is also expensive. The full sequence test identifies a common female ancestor in the last 400 years with 95% certainty.
This all means that in your case you could use YDNA or mtDNA to test for a relationship, and if you get a match you will have to fill in the gaps using traditional genealogy. I wouldn't think autosomal DNA testing is any use at all to you.