The yellow LED only lights up when a message is being sent. Does it light up when you press the “test” button? If it lights and then goes out, it means your tweet has gone through successfully. If it lights and then blinks, it means there was a communication error and the tweet did not go through.
If tweets are going through but the yellow LED never lights up, it’s possible that the LED is soldered in backwards. You want to make sure the positive leg of the LED, the anode, goes through the hole marked “+”. You can see here how to identify which side is positive.
Check those things, let us know how it goes, and we can take it from there!