LocalScript Working Online But Script Isn't Working Online(RemoteEvents, FE)?

I have a LocalScript that contains a Script and 2 RemoteEvents, first is called "Equip" and second is called "UnEquip." I have tried moving the events and the Script to multiple places, ReplicatedStorage, ServerStorage, Lighting even. The LocalScript fires the Equip event when the key "f" is clicked and then in the Script, it should find a model of a Sword in ReplicatedStorage and weld it to the Player's hand. I have found that the problem isn't to do with the LocalScript, I believe it is just a problem with the Script because everything in the LocalScript still runs smoothly and fine. I also went into the normal Play testing in Studio just to see if it worked there, and it does, it just won't work in online servers.

Here is my code:

LocalScript:

local Player = game.Players.LocalPlayer
local Character = Player.CharacterAdded:Wait()
local mouse = Player:GetMouse()
local Equipped = false
local UsedOnce = false

game:GetService("UserInputService").InputBegan:Connect(function(key)
    if key.KeyCode == Enum.KeyCode.F and Equipped ==  false and UsedOnce == false then
---Etc, etc, etc
script:WaitForChild("Equip") --Have tried it without WaitForChild as well
script.Equip:FireServer()
end)

Script:

UsedOnce = false
Equipped = false

script.Parent.Equip.OnServerEvent:Connect(function(Player)
        if Equipped == false and UsedOnce == false then
            wait()
        Equipped = true
        Staff = game.ReplicatedStorage.Weapons.Sword:Clone()
        Staff.Parent = Player.Character
        Staff:SetPrimaryPartCFrame(Player.Character.LeftHand.CFrame*CFrame.new(0, -0.15, 0))
        Staff:SetPrimaryPartCFrame(Staff.Handle.CFrame*CFrame.Angles(math.rad(90), 0, math.rad(90)))
        Welder = Instance.new("WeldConstraint")
        Welder.Parent = Staff.Handle
        Welder.Part0 = Staff.Handle
        Welder.Part1 = Player.Character.LeftHand
        ----------------------------------------------------------
        elseif Equipped ==  false and UsedOnce == true then
            wait()
        Equipped = true
        WelderBack:remove()
        Staff:SetPrimaryPartCFrame(Player.Character.LeftHand.CFrame*CFrame.new(0, 0, 0.2))
        Staff:SetPrimaryPartCFrame(Staff.Handle.CFrame*CFrame.Angles(math.rad(-90), math.rad(45), 0))
        WelderHand = Welder:Clone()
        WelderHand.Parent = Staff.Handle
        WelderHand.Part0 = Staff.Handle
        WelderHand.Part1 = Player.Character.LeftHand
        end
end)

script.Parent.UnEquip.OnServerEvent:Connect(function(Player)
    if UsedOnce == false then
        Welder:remove()
        elseif UsedOnce == true then
        WelderHand:remove()
    end
    wait()
        Staff:SetPrimaryPartCFrame(Player.Character.LowerTorso.CFrame*CFrame.new(1, 0.5, -2))
        Staff:SetPrimaryPartCFrame(Staff.Handle.CFrame*CFrame.Angles(math.rad(25), math.rad(90), 0))
        Staff:SetPrimaryPartCFrame(Staff.Handle.CFrame*CFrame.fromOrientation(math.rad(90), 0, 0))
        WelderBack = Welder:Clone()
        WelderBack.Parent = Staff.Handle
        WelderBack.Part0 = Staff.Handle
        WelderBack.Part1 = Player.Character.LowerTorso
        UsedOnce = true
        Equipped = false
end)

Please, any help?