Ok, done.

code/modules/modular_computers/computers/item/computer.dm

@@ -26,6 +26,7 @@
 	var/icon_state_unpowered = null							// Icon state when the computer is turned off.
 	var/icon_state_powered = null							// Icon state when the computer is turned on.
 	var/icon_state_menu = "menu"							// Icon state overlay when the computer is turned on, but no program is loaded that would override the screen.
+	var/display_overlays = TRUE								// If FALSE, don't draw overlays on this device at all
 	var/max_hardware_size = 0								// Maximal hardware w_class. Tablets/PDAs have 1, laptops 2, consoles 4.
 	var/steel_sheet_cost = 5								// Amount of steel sheets refunded when disassembling an empty frame of this computer.
 
@@ -208,20 +209,26 @@
 	else if(obj_integrity < max_integrity)
 		. += "<span class='warning'>It is damaged.</span>"
 
-/obj/item/modular_computer/update_icon()
-	cut_overlays()
+/obj/item/modular_computer/update_icon_state()
 	if(!enabled)
 		icon_state = icon_state_unpowered
 	else
 		icon_state = icon_state_powered
+
+
+/obj/item/modular_computer/update_overlays()
+	. = ..()
+	if(!display_overlays)
+		return
+	if(enabled)
 		if(active_program)
-			add_overlay(active_program.program_icon_state ? active_program.program_icon_state : icon_state_menu)
+			. += active_program.program_icon_state ? active_program.program_icon_state : icon_state_menu
 		else
-			add_overlay(icon_state_menu)
+			. += icon_state_menu
 
 	if(obj_integrity <= integrity_failure * max_integrity)
-		add_overlay("bsod")
-		add_overlay("broken")
+		. += "bsod"
+		. += "broken"
 
 
 // On-click handling. Turns on the computer if it's off and opens the GUI.

code/modules/modular_computers/computers/item/laptop.dm

@@ -18,6 +18,7 @@
 	screen_on = 0 		// Starts closed
 	var/start_open = TRUE	// unless this var is set to 1
 	var/icon_state_closed = "laptop-closed"
+	display_overlays = FALSE
 	var/w_class_open = WEIGHT_CLASS_BULKY
 
 /obj/item/modular_computer/laptop/examine(mob/user)
@@ -31,12 +32,11 @@
 	if(start_open && !screen_on)
 		toggle_open()
 
-/obj/item/modular_computer/laptop/update_icon()
-	if(screen_on)
-		..()
-	else
-		cut_overlays()
+/obj/item/modular_computer/laptop/update_icon_state()
+	if(!screen_on)
 		icon_state = icon_state_closed
+	else
+		. = ..()
 
 /obj/item/modular_computer/laptop/attack_self(mob/user)
 	if(!screen_on)
@@ -97,6 +97,7 @@
 		w_class = w_class_open
 
 	screen_on = !screen_on
+	display_overlays = screen_on
 	update_icon()
 
 

code/modules/modular_computers/computers/item/processor.dm

@@ -16,15 +16,15 @@
 		machinery_computer.cpu = null
 	machinery_computer = null
 
-/obj/item/modular_computer/processor/New(comp)
+/obj/item/modular_computer/processor/Initialize(mapload)
 	. = ..()
-	if(!comp || !istype(comp, /obj/machinery/modular_computer))
+	if(!loc || !istype(loc, /obj/machinery/modular_computer))
 		CRASH("Inapropriate type passed to obj/item/modular_computer/processor/New()! Aborting.")
 		return
 	// Obtain reference to machinery computer
 	all_components = list()
 	idle_threads = list()
-	machinery_computer = comp
+	machinery_computer = loc
 	machinery_computer.cpu = src
 	hardware_flag = machinery_computer.hardware_flag
 	max_hardware_size = machinery_computer.max_hardware_size
@@ -34,14 +34,11 @@
 	integrity_failure = machinery_computer.integrity_failure
 	base_active_power_usage = machinery_computer.base_active_power_usage
 	base_idle_power_usage = machinery_computer.base_idle_power_usage
+	machinery_computer.RegisterSignal(src, COMSIG_ATOM_UPDATED_ICON, /atom/proc/update_icon) //when we update_icon, also update the computer
 
 /obj/item/modular_computer/processor/relay_qdel()
 	qdel(machinery_computer)
 
-/obj/item/modular_computer/processor/update_icon()
-	if(machinery_computer)
-		return machinery_computer.update_icon()
-
 // This thing is not meant to be used on it's own, get topic data from our machinery owner.
 //obj/item/modular_computer/processor/canUseTopic(atom/movable/M, be_close=FALSE, no_dextery=FALSE, no_tk=FALSE)
 //	if(!machinery_computer)

code/modules/modular_computers/computers/item/tablet.dm

@@ -15,14 +15,11 @@
 	var/has_variants = TRUE
 	var/finish_color = null
 
-/obj/item/modular_computer/tablet/update_icon()
-	..()
+/obj/item/modular_computer/tablet/update_icon_state()
 	if(has_variants)
 		if(!finish_color)
 			finish_color = pick("red","blue","brown","green","black")
-		icon_state = "tablet-[finish_color]"
-		icon_state_unpowered = "tablet-[finish_color]"
-		icon_state_powered = "tablet-[finish_color]"
+		icon_state = icon_state_powered = icon_state_unpowered = "tablet-[finish_color]"
 
 /obj/item/modular_computer/tablet/syndicate_contract_uplink
 	name = "contractor tablet"

code/modules/modular_computers/computers/machinery/modular_computer.dm

@@ -48,26 +48,28 @@
 	if(cpu)
 		. |= cpu.emag_act(user)
 
-/obj/machinery/modular_computer/update_icon()
-	cut_overlays()
-	icon_state = icon_state_powered
+/obj/machinery/modular_computer/update_icon_state()
+	if(cpu?.enabled)
+		icon_state = icon_state_powered
+	else if(stat & NOPOWER || !(cpu?.use_power()))
+		icon_state = icon_state_unpowered
 
+/obj/machinery/modular_computer/update_overlays()
+	. = ..()
 	if(!cpu || !cpu.enabled)
 		if (!(stat & NOPOWER) && (cpu && cpu.use_power()))
-			add_overlay(screen_icon_screensaver)
-		else
-			icon_state = icon_state_unpowered
+			. += screen_icon_screensaver
 		set_light(0)
 	else
 		set_light(light_strength)
 		if(cpu.active_program)
-			add_overlay(cpu.active_program.program_icon_state ? cpu.active_program.program_icon_state : screen_icon_state_menu)
+			. += cpu.active_program.program_icon_state ? cpu.active_program.program_icon_state : screen_icon_state_menu
 		else
-			add_overlay(screen_icon_state_menu)
+			. += screen_icon_state_menu
 
 	if(cpu && cpu.obj_integrity <= cpu.integrity_failure * cpu.max_integrity)
-		add_overlay("bsod")
-		add_overlay("broken")
+		. += "bsod"
+		. += "broken"
 
 // Eject ID card from computer, if it has ID slot with card inside.
 /obj/machinery/modular_computer/proc/eject_id()