Shift register led display not working?
The power-up state of the HC595 is not defined, so it's normal for some random-looking set of flip-flop states to be present. 

You don't show any bypass capacitors in your circuit. The two oscillators are not synchronized in any way, so it might well be happening that they are locking to each other from disturbances caused by switching. 

You can try adding supply bypass capacitors (at least 100nF on each chip) and going with a ratio more like 3:1 than 2:1.