How to solve unresponsive buttons in Construct2

First of all, if you are going to use Cocoon.io to build your games, you should use sprites as buttons, do not use the Buttons object. If you used Buttons objects, then after compiling with Cocoon.io, the buttons will be invisible.

Next, make sure that the sprites for the buttons "Collisions" property is set to "Enabled". Next, for each sprite, make sure that the "Collision Polygon" is set to "Bounding Box". The default is set to follow the outline of the sprite - which is bad and reduces the surface area which can be touched. So set it to bounding box. See the picture below.