As said diodes only work in forward bias (in this case anyway) so you need to make sure you get the supply leads right (short leg cathode and also the part of the led 'lens' with a flat side is the cathode in case you've already cut the legs). Also, if you have got the connections the wrong way round and are resoldering them, be aware that LED's are also static and temperature sensitive, so you could have destroyed it by getting it too hot with additional soldering on short legs.
You can test the LED with a multimeter - use it on conitinuity setting and it will glow when forward biased.
