The hard stuff to which you refer is well-aged glazier's putty. This compound is used to hold glass panels in place in old fashioned aluminum window frames. Very soft and pliable when installed, the material naturally hardens until (after many years) it finally reaches the extremely brittle state you described.

The large chunks falling to the ground is your cue to scrape the remaining putty from each pane. Be careful the glass putty is all that holds the glass in. Then apply a new bead.

The trick to applying putty is its softness. Remove a palm-full from the can, knead it into a bead about the size of your small finger, force into where the glass and frame meet, and then use a glazier's knife or small putty knife to shape the putty at a 30 to 45 degree angle between the glass and the frame. By the way, this is an opportune time to replace scratched or damaged panes.