What's wrong with this level 1 easy script?!

script.Parent.Touched:connect(function()
	if game.StarterGui.Shop.Background.Visible == false
		then
		game.StarterGui.Shop.Background.Visible = true
	end
end)

--It's pretty simple, when someone clicks the brick, the background of a shopgui becomes visible. what's broken?

You said when they click the brick. In this situation you need a Clickdetector! Insert a click detector in the part. The code should be like this

The Function Is A OnClicked, Not An OnTouched

It Is Also Easier to Define and Could Make It More efficent

Background = game.StarterGui.Shop.Background

function onClicked(mouse)
    if Background.visible  == false
        then
        Background.Visible = true
    end
end

script.Parent.ClickDetector.MouseClick:connect(onClicked)

I Hope This Helped You!

script.Parent.ClickDetector.MouseClick:connect(function(plr)
	local player = game.Players:WaitForChild(plr.Name)
	local gui = player.PlayerGui
	
	if gui.Shop.Background.Visible == false then
		gui.Shop.Background.Visible = true
	else
		gui.Shop.Background.Visible = false
	end
end)

This problem is quite simple! You are accessing the StarterGui which is not what you want for live events. Instead you need the PlayerGui. This can be accomplished using the :GetPlayerFromCharacter() method

script.Parent.Touched:connect(function(hit)--Hit is what touches the part.
    if game.Players:GetPlayerFromCharacter(hit.Parent).PlayerGui.Shop.Background.Visible = false--we get the Player from game.Players
        then
game.Players:GetPlayerFromCharacter(hit.Parent).PlayerGui.Shop.Background.Visible = true
    end
end)

That should be it! Hope this helped!!!