If you are hearing two distinct clicks, and then you are also able to fire the gun when you manually cock it, the sear is not the problem. It would seem the sear spring itself has at least enough tension to allow the sear to engage the hammer.
And what I meant by "the hammer following the slide into battery" is that the hammer is following the slide down and automatically putting itself in the "uncocked" position. That would indicate that the sear is not catching the hammer during the relatively violent (by comparison to hand cycling) recoil cycle when firing.
I'm still not clear if, when you manually cock the hammer, then fire, the hammer is remaining at full cock position or not. The fact that you are able to manually cock and fire one round tells me that the sear itself is OK.
Here's another thing to check: Field strip the gun, then look at the small vertical bar ("trigger lever") that is attached to the rear of the trigger. Pull the trigger and watch the trigger lever bar rise up from the frame. Now, while holding the trigger back, see if the trigger lever moves forward freely by pushing on it. It should also snap back to its rearward position when you let go of it.
Also, while you have the slide off, look at the pivoting bar that is held in place by the pin that goes through the slide. The small "bump" (or hump, if you prefer) should be at the rear of the lever if it was installed correctly, although, if, as you stated, you are able to manually cock the hammer and fire one round it seems to be correctly oriented.
My best guess still is, IF the hammer is following the slide forward and ending up in the UNCOCKED position after you fire the one round, you have a weak sear spring. It's easy enough to change, but you need a strong thumb, a small punch, a strong index finger and a little patience.
