For testing you may want to try something like a 10uf cap as C3 (plus towards pin 6/7) and 47K as R2 to give you a long time constant (around .5 sec) of output pulse. Then a tap on the trigger should give you a fairly long led on time before it goes off. With a short output pulse it may be hard to tell if it is working or not (although it does sound like you have some bad 555s).
Peter