Well unless he has one of those protected cells that fell into protected mode at like 2V it should be enough even at the discharged 3.6V to power the green. Even 2.6V should be enough for TTL which is way below the discharged voltage of those LiPo batteries..
STA: Now try connecting the two leads on the blue. Maybe it's active low? You could also try flipping the connection with the battery. Maybe the leads are backwards?
Finally, if it still doesn't light up, face the output towards some white paper and use a digital camera to see if you can see any light coming out via what it shows in the viewfinder. That light would be the infrared, which digital cameras can see. Don't use your eyes directly.