If it is wired up as in the drawing the LEDs are burned out. There might have been a short bright blink the first time the relay changed. You need something like a 1K to 10K resistor in series with the LED(s).
Are you sure the load is connected correctly? If you connect 5V to NO and the load to NC, it will never work. 5V OR the load must be connected to the C pin, and the other to NO or NC, depending on if you want to switch it on or switch it off. Is the led orientated the correct way (Anode to positive, cathode to negative (ground)? Do you have a current limiting resistor in series with the led? If not, 5v will blow the led and make it junk.