Why won't my changed function work?

You're only connecting a function to the Changed event of only one of the objects. You would need to have a separate Changed event for all of the values.

FanOnOne=game.Workspace.FanValues.One
FanOnTwo=game.Workspace.FanValues.Two
FanOnThree=game.Workspace.FanValues.Three
FanOff=game.Workspace.FanValues.Off

FanOnOne.Changed:connect(function()
    if FanOnOne.Value == true then -- NUMBER 1
        script.Parent.Text = "Fan Power: One"
    end
end)

FanOnTwo.Changed:connect(function()
    if FanOnTwo.Value == true then -- NUMBER 1
        script.Parent.Text = "Fan Power: Two"
    end
end)

--And so on...

An easier way to do this:

You could make what you're doing easier by putting all your value objects into a table and then use a for loop to connect a function to the Changed event of each item in the table.

FanValues = {game.Workspace.FanValues.One, game.Workspace.FanValues.Two, game.Workspace.FanValues.Three, game.Workspace.FanValues.Off} --FanValues all in a table.

for i,v in pairs(FanValues) do --Loop through all of the values in the table
    ypcall(function() --Stops the script from breaking if it errors, allows yielding as opposed to pcall.
        v.Changed:connect(function() --Connects a function to the Changed event of the value of the table that the for loop is currently looping through. 
            if v.Value == true then --If the value of the object is true then
                script.Parent.Text = "Fan Power: "..v.Name --Sets the Text of the script's parent to "Fan Power: " then the name of the value object.
            end
        end)
    end)
end

Click here for more information on pcall()

Click here for more information on ypcall()