Anyone know how to fix this Terminal core script?

It's hard to read your code if it isn't tabbed optimally.

local button        = script.Parent
local player        = button.Parent.Parent.Parent.Parent
ownervalue          = player.PlayerGui.TermTimer.TOwner.Text
timevalue           = player.PlayerGui.TermTimer.Time.Text
CapTime             = game.Workspace.ICFTerminal.TermCapSystem.CapTime
-- A variable shouldn't be referred to a property, unless if you want to access its value!
a                   = game.Workspace.ICFTerminal.TermCapSystem.Activator
hah                 = game.Workspace.ICFTerminal.TermCapSystem.Hah
t1                  = game.Workspace.ICFTerminal.TermCapSystem.TeamPart1
t2                  = game.Workspace.ICFTerminal.TermCapSystem.TeamPart2
am                  = game.Workspace.ICFTerminal.TermCapSystem.Activator.Mesh
sm1                 = game.Workspace.ICFTerminal.SmokeParts.smoke1.Smoke
sm2                 = game.Workspace.ICFTerminal.SmokeParts.smoke2.Smoke
sm3                 = game.Workspace.ICFTerminal.SmokeParts.smoke3.Smoke
sm4                 = game.Workspace.ICFTerminal.SmokeParts.smoke4.Smoke

function OnClicked()
    if player.TeamColor == ("Bright red") then
        m = Instance.new("Message", workspace) -- Parent the Message!
        m.Text = "The Terminal is being captured by the Raiders!"
        wait(5)
        m:Destroy()

--First Step: Changing Colors--

        a.BrickColor = player.TeamColor
        hah.BrickColor = player.TeamColor
        t1.BrickColor = player.TeamColor
        t2.BrickColor = player.TeamColor
        wait(.1)

--Next Step: Activating Smoke--

        sm1.Enabled = true
        sm2.Enabled = true
        sm3.Enabled = true
        sm4.Enabled = true

--Step Three: Enabling Timer--

        CapTime.Value = 0
        ownervalue = "Raiders"

        while true do
            timevalue = CapTime.Value + 1
            wait(1)
        end
    end
end

button.MouseButton1Down:connect(onClicked)
-- You already referred "script.Parent" to a variable named as "button". Use that instead of the former, to increase efficiency.
-- This is the only error I see. This is called a logical error, where no error messages return, but the script is doing what you don't expect it to do.

The ":connect()" method accepts a function as its argument.

It is more ideal to use a LocalScript when accessing the PlayerGui. Also, you needed to call the OnClicked function so I have done so for you. I have also make the script a bit more efficient by accessing the player through game.Players.LocalPlayer. If the script has issues or you have more questions, please let me know.

local button = script.Parent
local player = game.Players.LocalPlayer
ownervalue = player.PlayerGui.TermTimer.TOwner.Text
timevalue = player.PlayerGui.TermTimer.Time.Text
terminal = game.workspace.ICFTerminal
CapTime = terminal.TermCapSystem.CapTime
a = terminal.TermCapSystem.Activator
hah   = terminal.TermCapSystem.Hah
t1 = terminal.TermCapSystem.TeamPart1
t2 = terminal.TermCapSystem.TeamPart2
am = terminal.TermCapSystem.Activator.Mesh
sm1 = terminal.SmokeParts.smoke1.Smoke
sm2 = terminal.SmokeParts.smoke2.Smoke
sm3 = terminal.SmokeParts.smoke3.Smoke
sm4 = terminal.SmokeParts.smoke4.Smoke

button.MouseButton1Down:connect(function()
    if player.TeamColor == ("Bright red") then
            m = Instance.new("Message")
            m.Text = "The Terminal is being captured by the Raiders!"
            wait(5)
            m:Destroy()
        --First Step: Changing Colors--
         a.BrickColor = player.TeamColor
         hah.BrickColor = player.TeamColor
         t1.BrickColor = player.TeamColor
         t2.BrickColor = player.TeamColor
            wait(.1)
        --Next Step: Activating Smoke--
        sm1.Enabled = true
        sm2.Enabled = true
        sm3.Enabled = true
        sm4.Enabled = true
        --Step Three: Enabling Timer--
            CapTime.Value = 0
            ownervalue = "Raiders"
        while true do
                timevalue = CapTime.Value + 1
            wait(1)
        end
    end
end)