I just bought a relay, here is the relay: http://www.seeedstudio.com/wiki/GROVE_-_Starter_Kit_V1.0b
I connect the pin D1 to the pin 7 Arduino, then pin Com to 5V, then pin ON to the LED, then pin VCC to 5V, then pin GND to GND Arduino.
I'm still confused. You're the only person who has suggested which relay you're using, and you have only identified it by reference to the GROVE starter kit. Are you saying now that your relay is not the one from the GROVE starter kit?
So the LED you wired up is OFF? You do know that D1(pin 7) turns the relay on and off, right. Also that relay is normally closed when its not being powered, which means the LED should be lit. If D1 is always HIGH then the relay is open, and the LED is OFF.
Now if the Onboard LED is also off then it could be that the 5 volts is not enought to power it.