What is wrong with this GUI? (Solved)

There is a much simpler way to organize this.

function onClicked()
    On = not On;
    -- switches `On` between `true` and `false`
end

script.Parent.MouseButton1Down:connect(onClicked)

while wait(0) do
    local tex = "rbxassetid://173364314";
    if On then
        tex = "rbxassetid://173364351";
    end
    script.Parent.Image = tex;
end

This avoids the loops inside of the OnClicked and makes it much, much clearer.

At this point, though, we'll see that the loop itself is redundant. It only changes whenever On changes, so we can just move the if into the onClicked function:

function onClicked()
    On = not On;
    local tex = "rbxassetid://173364314";
    if On then
        tex = "rbxassetid://173364351";
    end
    script.Parent.Image = tex;
end

script.Parent.MouseButton1Down:connect(onClicked)

And now we have a much, much simpler, cleaner solution. (The first snippet could be used if there was some sort of animation that was dependant on whether or not it was on; the second one lacks this functionality)

On=false 
function onClicked() 
    if On == false then
        On = true 
        while On == true do
            script.Parent.Image = "http://www.roblox.com/asset/?id=173364351"
            wait(0) 
            on = false -- You forgot to set on as false.
        while On == false do -- You needed on to be false to allow this to work.
            script.Parent.Image = "http://www.roblox.com/asset/?id=173364314"
            wait(0)
        end  
        end
    end
end


script.Parent.MouseButton1Down:connect(onClicked)

You forgot to set on as false after the first part. I'm not sure if this may also affect it, but maybe you should use an if/else script since it seems that the button may break when clicked though I'm not sure about it. Just try this script for now and if there are any problems tell me. :D