The handbrake pulls viua steelcables two brakesegments in a special drum mounted together with the brakedisk on each rear wheel.
The problem sounds familiar to me.

Of course you have to check first if the cables move freely.
Then check if the adjustment is correct (3 teeth and then the action starts)

If the problem persists, there are two possibilities:
1.The brakepads are worn
2. One or more brakepads have come loose from the segment.This is what happened to me.
In both cases you have to replace all 4 brakepads.
good luck
John