Not to worry, 23 and me has determined that they found Neanderthal in all of us but getting past the second cousins in a bit iffy.
Not everything is as always it seems, heh heh... sometimes there are woodpile problems... also, second cousins have at least one great-grandparent in common, thirds have at least one great-great-grandparent in common, and there are already sixteen of those. By 4th-greats, there are 64, and only 46 chromosome halves among them. Even in situations with no half-sibling generations, it's not unlikely that things could fall out.
My Ancestry DNA showed no DNA in common between my parents, but they are both descended from three sisters (one on dad's, two on mom's), of course it's quite a few hops skips and jumps (nearly 400 years).
Is it possible to get DNA from cremains?