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Now that's a project..

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Maybe the 555 doesn't need a reset when power is applied.

Now most of it is fixed, except the output of the 555 is low and puts R5 across the LED so that it can't give an output when there is light.

This will finish it: "Also, you'll need a diode in series with R5 because when pin3 of the 555 is low it will drain any voltage (through R5) that the LED produces when sensing light." Because your circuit doesn't have the transistor in the original circuit.
 
hmmm... it still does the same :( . I'll have to think about this some more, ...go through the other ideas.
 
The diode in series with R5 must have its cathode to the LED.
You need a very bright light with the same color as the LED for the LED to make enough voltage to change the comparator.
 
There is another problem that I didn't think of yesterday and that is the issue of the LM358s input bias current. It can range from a typical 45na to a max of 100na which would produce a voltage of 0.21V to 0.47V across the 4M7 resistor (LM358 pin5). This exceeds the bias voltage of 0.033V on pin6 of the LM358 so the output of the LM358 will never switch states! For clairity, I will refer to your original diagram you posted. What you need to do is pull the LED and the 555 out of the circuit. Then increase the resistance of R2 until pin7 of the LM358 goes low (Or pin2 of 74hct04 goes high) Now you can put the LED back in the circuit. Now check to see if pin7 of the LM358 toggles when you expose the LED to light/dark (Try a flashlight). Once you have this working you can put the 555 back in and we can troubleshoot the rest of the circuit. Divide and conquer!
 
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