I couldn't tell you and am not sure what you'd try other than getting another bulb to test it. Probably there is some way to test if the circuit is good with a circuit tester, but that is beyond my skill! Oh duh - first thing would be to try the "dead" bulb in a working slot of your fixture, that will tell you if its the bulb or the fixture.
Now my brother, who is an electrical engineer and all around computer nerd and expert told me that all electronics live by the power of blue smoke and, when the blue smoke escapes, your electronics die. It does sound rather like a "death by the loss of blue smoke" scenario, but not now you need to find out if it is the bulb that died or the fixture! I know when the blue smoke escaped my last computer monitor, there was no more life in it... hehe