Ok, we`re making progress ! Using one NOR gate from the 7002 as an inverter is exactly what you need. Although in this case, the QH output of the 164 doesn't need a pull-down resistor beacause the 164 outputs are always driven to a valid logic level (0 or 1). Also, you don't need the diode for the second input of the NOR gate. A simple way to hook up NOR or NAND gate as inverters is simply to send your signal (QH) to both inputs. Do the logic table to convince yourself !!
Using a pull-down along with your button to make the clock is exactly what we are looking for. In your diagram, however, the pull-down is not quite wired properly (small mistake I guess !!). It must be between clock and ground. As for the A input, there is a little problem. Remember that the sequential ICs sample and compute their output
before the clock edge and update them
during the clock edge. So in your case, if you change the value of A from 0 to 1 at the same time as the clock edge occurs, the circuit won't see the "1" but will instead inject a "0" at the output. The A input needs to be stable before the clock edge. And in this first stage, you always need to inject the same thing, don't you ? Should be simple !!
Hooking the unused input of the 7002 to ground is also good. But we'll soon use them too !!
Using decoupling (or bypass) capacitors for your Vcc is also a good thing. But bypass capacitors must be put in parallel with the source, not in series like you did.
Another thing you could look at, at this point, is the value of the current limiting resistors for your LEDs. 56Ω seems a bit low. Remember that you want to run them at 10-20 mA each.
And finally, what did you have in mind when adding the two resistors in series with the ICs power ?
Let me know !