There should be three turrets in the enclosures. The deal is that two of the enclosures are controlled (opened?) with one button, and one is opened with another.
And once you made it through the battle, I should hope that Alyx comes for you; you deserve it.
There are several threads on these forums dedicated to this issue. It seems that you (as well as quite a few other people) have somehow taken an alternative route and have ended up rather backwards in the level. Poke through the "Steam & HL2 Support" forums to find your solution.
The "garbage squisher" is actually the combine, a living machine. The obvious answer is that you need to get out of there. The immediate answer is, how?
Don't try to destroy the helicopter with your conventional weapons. Just use the large containers for cover and take out all the guards. Eventually you'll make your way to the tower (see you screenshot) where there will be some mounted machine guns that will get rid of the helicopter...