Software
You could use the wiringPi library(you may have to install it) as described in this questionquestion. It tests input, output, pull-up and pull-down. It will return Failed user gpios: None
if all your pins are OK.
Hardware
Also, if it returns all clear, make sure that you are observing polarity for LED3. In other words, if you have it in the wrong way it will not work(longer lead is positive).