GUI Function on TextButton...who can help?

It's good practice to only have one script for the local player and the server.

Having a hundred scripts that only handle a single button is very messy and makes it harder to edit, update and correct things later.

That aside,

It appears that you are searching for "PartZero", however the part's name is changed to "Rotator" and as such the script can't account for it.

Given the lack of information about how it's structured I'll suggest this:

--Parent the script to the ScreenGui for neater code (Should really be in PlayerGui but that aside)
script.Parent = game.Players.LocalPlayer.PlayerGui.ScreenGui

local PartZero = game.Players.LocalPlayer.PartZero
local OpenButton = game.Players.LocalPlayer.PlayerGui.ScreenGui.Frame.Open

OpenButton.MouseButton1Click:Connect(function()
    PartZero.Motor.DesiredAngle = -1.5
end)

This is assuming of course that the "PartZero" is located in the player based on what little information you have provided. It really shouldn't be in there, this might be the problem. Assuming it is the problem simply change the location for PartZero to where it actually is located.

If the part is in the workspace, then you need to check if the game is FilteringEnabled. If it isn't, then you can simply change the PartZero variable to workspace.PartZero If it is, then you'll need to handle it with a event. Like so:

--Server Script
local PartZero = workspace.PartZero

game.ReplicatedStorage.MotorChange.OnServerEvent:Connect(function(player)
    PartZero.Motor.DesiredAngle = -1.5
end)

--Local Script
local OpenButton = game.Players.LocalPlayer.PlayerGui.ScreenGui.Frame.Open
local ButtonDelay = 0.1 --Cooldown for the button

local Debounce = false
OpenButton.MouseButton1Click:Connect(function()
    if Debounce == false then
        Debounce = true
        game.ReplicatedStorage.MotorChange.FireServer()
        wait(ButtonDelay)
        Debounce = false
    end
end)

If this is unhelpful, then more information may be required.