PWM Dimming 24v with 3.3v input
The 74HCT595 has an enable input on pin 19. You need to connect this pin to GND in order to enable the outputs.

It look like you have left this pin floating (disconnected), meaning that as a TTL input it will float high and thus your outputs will be disabled. 

You can either connect the pin directly to GND, or use a pull down resistor (10k would be a suitable value).