Problem with a voltage follower transistor circuit
From your description, I assume that you are trying to visualice the output voltage variation through the LED light intensity.

That is not an easy thing to do, because the eye's dynamic ranges prevents you from noticing any LED's luminous intensity variation. Your LED is in fact varying it's intensity, but not enough to be noticed ant naked eye.

In respect to removing the opamp: That's because some parasitic current is being injected through the base, making the transistors keep conducting and thus keeping the LED ON.