I believe this is Puzzle #9. You need to have the alchemy lab restored, Puzzle #8 completed, Lvl 3 Restoration, Lvl 3 Leadership (for your tribal chief), and a Master Builder.
First, drag ur Master builder to the chalkboard in the achemy lab to draw out the plans for rebuilding the statue. Next, drag any villager with some building skills to start working on the scaffold close to the base of the broken statue (its gonna be up the hill where it curves closest to the statue). When you have him/her over the correct spot, the status bar will read " This will be a good place to anchor the statue".
When the scaffold is complete, you need to get your tribal chief to start the other villagers to work on pushing the top part of the statue up the hill. This wil take some time, but its a great way to get some of your rookie builders up to par. Also, make sure you tribal chief doesnt get distracted; otherwise, the other villagers will leave the project abandoned. The more builders you have working on it, the less time to complete. I think I had about 6 villagers until the status bar read "No more room to work".
By the way, after this statue is restored, you will find another 'key' near the foot of the statue (where to top portion once lay). I hope this helps and stay on those villagers; they get distracted really easy!
This information comes from jayisgames.com, so all the credit goes to them:
Repairing the Statue: Prerequisites: Level 3 Restoration, Level 3 Leadership, completed Puzzle #8, a Chief, lots of trained builders. Make sure the bath is totally completed, at which point the plans will disappear from the lab chalkboard. Drop a Master Builder on the chalkboard again to draw plan for repairing the statue. Then, fly a Master Builder over the stone path to the key door. At some point, the builder will "see a good place to anchor the statue." Drop him on that spot and he or she will build the scaffolding. Then, drop your chief onto the statue to direct work. Put as many builders as you have free onto this project, which takes a really long time. They will slooooooowly inch the statue up the hill and back into position. http://jayisgames.com/archives/2008/05/virtual_villagers_3_the_secret_city.php
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