Go back to the gardens. There you'll find a water station. Use your wrench on it, and pull to open the water valve to the Croft Mansion.
Go into one of the fountains and use your water bucket in it, to fill it up with water.
Now get back to the mansion's living room.
Climb the boxes to the top.
Jump and grab the painting.
Go to the other side, climb to the top of the boxes, and grab that cog wheel.