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.