I think it's best to reload from a previous save game, preferably one where Barney and the last batch are still with you in the middle of the transport map.
You do have a recent save game, don't you? Otherwise the only thing you can do is restart the whole chapter. That doesn't sound so good...
Push her around a bit, use her (press E, you dirty fellow). Barney's waiting for Alyx to close the door so that the script can be set in motion.
As vikram says, try walking to the other door. Something needs to happen.
Or, that everything G-man has (and his superiors have) made ol' Gordie do is evil in its intent and purpose as well as eventual outcome.
Good guy finds out he's fighting the bad fight. Works for me. Much, much better than the old theatrical hero dies ending.
I've found that the best way to beat that level, and all Zombines in general, especially in the dark, is to point your flashlight and run towards them, preferably with a shotgun.
You do two things by doing this: first, you let Alyx aim at them properly, and second, once they're dead, you have...
I'm having this problem as well, but only after the credits are finished. I can't see the end sneak peek video
(And, for clarification, I've been here long enough, and am not stupid enough, to a. not have performed a search, and b. not having an original copy of the game. I found out how to...