Using Touched and TouchEnded to change value in GUI?

Scripts can't acces PlayerUI. You'll have to fire a RemoteEvent, which a localscript will trigger from. This way, you can tell a specific client, to do something, so the server doesn't have to do it. (You most likely want to handle anything UI related to the client.)

Example:

--script
Part.Touched:Connect(function(a)
	--Check if player
	if game.Players:GetPlayerFromCharacter(a.Parent) then
	--The "true" here, is "state" in the localscript. (First argument)
		game.ReplicatedStorage.RemoteEvent:FireClient(game.Players[a.Parent.Name], true)
	end
end)

Part.TouchEnded:Connect(function(a)
	--Check if player
	if game.Players:GetPlayerFromCharacter(a.Parent) then
	--The "false" here, is "state" in the localscript. (First argument)
		game.ReplicatedStorage.RemoteEvent:FireClient(game.Players[a.Parent.Name], false)
	end
end)

--localscript
game.ReplicatedStorage.RemoteEvent.OnClientEvent:Connect(function(state)
	game.Players.LocalPlayer.PlayerGui.ComputerGui.Battery.change.charging.Value = state
end)

--Structure
--[[

game
-Workspace
--Part
---Script

-ReplicatedStorage
--RemoteEvent

-StarterGui
--LocalScript
--ComputerGui

]]

--I haven't tested this code, so if anything errors, or something unexpected happens, feel free to comment on it.