Touching certain pins (grounding body capacitance) causing pcb to work
the 100pF  model is only for the arc of a finger tip with ESD.
I can get 1000 pF easily with my fingers pressing on an LCR meter.


In any case your layour probably lacks basic EMI controls for ground plane, excessive long inductive jumpers to the switch and perhaps missing decoupling caps on Vcc to Vdd.


try these methods


add decoupling cap on Vcc (.1uF ) Pin 4 &amp; 1 for each IC and >=10uF
twist all long wires (signal, switched power and ground return)



If your wiring layout looked anything like the logic diagram , it would never work due to inductive effects crosstalk glitches. 

Show photo's or study how to layout a breadboard.