My Emergency coolant is not working?

I'm struggling to understand your question here, but if you want to wait a certain amount of time that is in a value, you could do something like:

local value = game.Workspace.Wait.Value

wait(value) --This will wait however long the value is - make sure it is a NumberValue or IntValue!

For the button pressing, you could use a ClickDetector in a brick

function onClicked(playerWhoClicked)
    --Run the cooldown/meltdown function
end

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

So the full script would be:

function onClicked(playerWhoClicked)
    --Run the cooldown/meltdown function
if workspace:FindFirstChild("EmergencyGlass")~= nil then
    game.Workspace.EmergencyGlass:Destroy()
end
local g = Instance.new("Hint",game.Workspace)
        g.Text = "Emergency coolant activated!"
        wait(19)
        g:Destroy()
        local msg = Instance.new("Message")
    msg.Parent = game.Workspace
    msg.Name = 'OMG'
    msg.Text = "Self destruct sequence aborted."
    wait(24)
    msg.Text = "Warning Coolant unable to reach core. Self Destruct sequence re-intiated."
    game.Workspace.Gate.Countdown.Value.Value =40
    wait(14)
    if game.Workspace:FindFirstChild("OMG")~=nil then
        game.Workspace.OMG:remove()
    end
game.Workspace.Gate.Countdown.Disabled = true
end

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

If this helps, please "Accept Answer" - if not, be sure to comment with another clearer explanation of what you mean!