My cake crumbled on the top and took very long time to cook
Brown sugar contains molasses, which is acidic, and probably threw off the acid-base balance in the cake. It also contains more water than white sugar, but neither contain much, so that probably didn't matter.

Did the cake rise as expected? I'm guessing “no”, which is probably what changed the baking time.

Quickly looking it up, between ¼ tsp and ½ tsp of baking soda would neutralize the brown sugar, if you feel like trying again.

Other possibilities:


your baking powder or soda is too old; how long ago was the last cake? Baking powder especially has a limited shelf-life.
mistakes (oven temperature set wrong, measured wrong)