Why is my shift to sprint script not making my character run?

First of all, try to make ":Connect" into ":connect", and maybe that will help.

Second of all, use

if KeyDown:byte() == 19 then

on those things instead of

if KeyDown == 19 then

It seems to work for me, I used a script in a game I'm making with that sort of idea:

local mouse = game.Players.LocalPlayer:GetMouse()

function onkeyDown(key)
	if key:byte() == 19 then
		if script.Parent.CurrentOption.Value == "Fight" then
			script.Parent.CurrentOption.Value = "Act"
			script.Parent.Fight.Image = "rbxgameasset://Images/spr_fightbt_center_0"
			script.Parent.Act.Image = "rbxgameasset://Images/spr_actbt_center_1"
			script.Parent.Act.Heart.Visible = true
			script.Parent.Fight.Heart.Visible = false
		elseif script.Parent.CurrentOption.Value == "Act" then
			script.Parent.CurrentOption.Value = "Item"
			script.Parent.Act.Image = "rbxgameasset://Images/spr_actbt_center_0"
			script.Parent.Item.Image = "rbxgameasset://Images/spr_itembt_1"
			script.Parent.Item.Heart.Visible = true
			script.Parent.Act.Heart.Visible = false
		elseif script.Parent.CurrentOption.Value == "Item" then
			script.Parent.CurrentOption.Value = "Mercy"
			script.Parent.Item.Image = "rbxgameasset://Images/spr_itembt_0"
			script.Parent.Mercy.Image = "rbxgameasset://Images/spr_sparebt_1"
			script.Parent.Mercy.Heart.Visible = true
			script.Parent.Item.Heart.Visible = false
		elseif script.Parent.CurrentOption.Value == "Mercy" then
			script.Parent.CurrentOption.Value = "Fight"
			script.Parent.Mercy.Image = "rbxgameasset://Images/spr_sparebt_0"
			script.Parent.Fight.Image = "rbxgameasset://Images/spr_fightbt_center_1"
			script.Parent.Fight.Heart.Visible = true
			script.Parent.Mercy.Heart.Visible = false
		end
	end 
end

mouse.KeyDown:connect(onkeyDown)