What purpose does the yellow and green LEDs have on the Arduino? I have wired up a small project with a shift register (see below), but depending on how I put the 74HC595 IC (8-bit shift register with 3-state output register), the green and yellow LEDs of the Arduino stop shining.

What are these LEDs for? Do they tell something about a possible damage of the IC/short circuit in the setup?
The green LED is marked with ON, and it indicates that the Arduino has power.

The yellow LED is marked L and is just connected to pin 13. So when you set pin 13 to HIGH the LED lights up. You can however still use pin 13 for other things.

When the green LED stops shining you most likely have a short somewhere. As the short will drain all power away, so the Arduino has no power left to light the LED(s).