Definitely one of the more annoying quests out there.
Basically how I did it was write it down on a piece of paper noting which 1 was on and which 1 was off.
After that my main goal was to make sure they were all off, so I could have a fresh start.
From there it's simple. Once you have all the pillars off, hit every pillar that is NOT connected to the center pillar in a clockwise rotation. After that hit the center pillar and bam. The turret is on.
Forthing you're a freaking magician. I'm going to go back and give that a shot. It's funny to me to find another thread about how much this quest sucks since I just made one this afternoon. I felt very defeated and discouraged after giving the quest many hours of my time and having to give up in the end. I'll give your suggestion a shot and I'll send you 10 internets in the mail if it works.
Edit: Ok, now I can't get the f*cking lights off. /tableflip. I just realized how much I dislike this game. It feels very claustrophobic to me because of the way the camera works. The very fact that I can't pull my camera any farther than a couple feet from my character makes me feel like it's stuck in cement. This quest would be so much easier if lights stayed on and you could actually view the whole field. So many things about this game have been nagging me, and honestly, pandas are starting to look pretty good right now :S