I might. Cork in your whisky might be okay if you drink it up quickly, but there has certainly been plenty of discussion here about not laying your bottles down, simply to avoid contact between liquid and cork. I suspect this bottle was on its side for some time. Does it taste right to you? Can you exchange it for another bottle of same? If I had any doubt, and could exchange it, I would. You paid enough for it, it should be right.
Musky, Lawrence's advice is meant specifically to get the crumbling cork out of contact with the whisky, which is indeed good advice if Jdiddy decides to keep the bottle.
Jdiddy, if you must keep it, you might consider decanting it. You could filter it through a coarse filter, rinse and dry the bottle, and return it thereto, if you want.