How to change ignition control module - 1991 Buick LeSabre

Question edited for clarity and spelling 'module'..
Question moved to model category.

My research only shows one connector on the ignition control module.

https://www.google.com/search?q=2003+Buick+Rendezvous+ignition+control+module+connectors

Videos on replacing the ICM.

https://www.google.com/search?q=2003+Buick+Rendezvous+ignition+control+module+replacement

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Could be ignition switch problem or a stuck closed relay . Gm has had ignition switch problems . Your best bet , if you don't know how to test automotive electrical systems , mite be to take it to a qualified repair shop. With the electronic's on your vehicle ,really ,it could anything .The BCM - body control module controls most of the vehicle .
On vehicles that have several control modules connected by serial data circuits, one module is the power mode master (PMM). On this vehicle the PMM is the body control module (BCM). The BCM uses 3 signals from the ignition switch. These are the Ignition 0, Ignition 1, and Accessory.
To determine the correct power mode the BCM uses:
• The state of these signals
• The sequence of switch closures received by the BCM
• The status of the engine run flag

Fail-safe Operation
Since the operation of the vehicle systems depends on the power mode, there is a fail-safe plan in place should the body control module (BCM) fail to send a power mode message. The fail-safe plan covers modules with discrete ignition signal inputs as well as those modules using exclusively serial data control of power mode.
Serial Data Messages
The modules that depend exclusively on serial data messages for power modes stay in the state dictated by the last valid BCM message until they receive the engine status from the powertrain control module (PCM). If the BCM fails, the modules monitor the serial data circuit for the engine run flag serial data. If the engine run flag serial data is true, indicating that the engine is running, the modules fail-safe to Run. In this state the modules and their subsystems can support all operator requirements. If the engine run flag serial data is false, indicating that the engine is not running, the modules fail-safe to OFF-AWAKE. In this state the modules are constantly checking for a change status message on the serial data circuits and can respond to both local inputs and serial data inputs from other modules on the vehicle.
Discrete Ignition Signals
Those modules that have discrete ignition signal inputs also remain in the state dictated by the last valid BCM message received on the serial data circuits. They then check the state of their discrete ignition input to determine the current valid state. If the discrete ignition input is active, B+, the modules will fail-safe to the RUN power mode. If the discrete ignition input is not active, open or 0 voltage, the modules will fail-safe to OFF-AWAKE. In this state the modules are constantly checking for a change status message on the serial data circuits and can respond to both local inputs and serial data inputs from other modules on the vehicle.

http://www.bbbind.com/free_tsb.html free wiring diagrams . Ignition switch or ignition system - coils , plugs , wires etc... .
Everything on your vehicle is electronically controlled by the BCM - body control module .
On vehicles that have several control modules connected by serial data circuits, one module is the power mode master (PMM). On this vehicle the PMM is the body control module (BCM). The BCM uses 3 signals from the ignition switch. These are the Ignition 0, Ignition 1, and Accessory.
Discrete Ignition Signals
Those modules that have discrete ignition signal inputs also remain in the state dictated by the last valid BCM message received on the serial data circuits. They then check the state of their discrete ignition input to determine the current valid state. If the discrete ignition input is active, B+, the modules will fail-safe to the RUN power mode. If the discrete ignition input is not active, open or 0 voltage, the modules will fail-safe to OFF-AWAKE. In this state the modules are constantly checking for a change status message on the serial data circuits and can respond to both local inputs and serial data inputs from other modules on the vehicle.
Your best bet , take it to a qualified repair shop !

Starter switch ? You do mean ignition switch , the thing on the dash or steering column that you stick the key in ! You car not starting ? The ignition switch isn't the same anymore , sends Discrete Ignition Signals to a module ,in the case of your vehicle it is the DIM - dash integrated module.
The body control system consists of the following 3 modules:
?€¢
The dash integration module (DIM)

?€¢
The instrument panel integration module (IPM)

?€¢
The rear integration module (RIM)

Each of the 3 body control modules integrate a number of functional systems under the control of a single module. Each of the modules are connected to the Class 2 serial data line; many control signals are implemented by Class 2 messages.
On vehicles that have several control modules connected by serial data circuits, one module is the power mode master (PMM). On this vehicle the PMM is the DIM. The PMM receives 4 signals from the ignition switch.
To determine the correct power mode the PMM uses the following circuits:
?€¢
Accessory voltage

?€¢
Ignition 1 voltage

?€¢
Ignition 3 voltage

?€¢
Off/Run/Crank voltage

Your best bet would be to take to a repair shop that has knowledge of this type system . You probably don't need an ignition switch.
Discrete Ignition Signals Those modules that have discrete ignition signal inputs also remain in the state dictated by the last valid PMM message received on the serial data circuits. They then check the state of their discrete ignition input to determine the current valid state. If the discrete ignition input is active, battery positive voltage, the modules will fail-safe to the RUN power mode. If the discrete ignition input is not active, open or 0 voltage, the modules will fail-safe to OFF-AWAKE. In this state the modules are constantly checking for a change status message on the serial data circuits and can respond to both local inputs and serial data inputs from other modules on the vehicle.

1994 Chevrolet Camaro 3.4L SFI 6cyl

The Control Module-Ignition is located: Under hood, center, front engine area, below valve cover, mounted in distributorless ignition assembly

1994 Chevrolet Camaro 5.7L SFI OHV 8cyl

The Control Module-Ignition is located: Under hood, center, rear engine area, mounted in distributor

Before replacing the coil , to make sure that's what's wrong ,switch it to another cylinder to see if the problem moves to that cylinder ! This DTC is for a circuit control problem , DTC P0353: Ignition Coil 3 Control Circuit
I have seen lose wire connections cause misfires , there is a four wire connector at the coil marked A,B,C,D . C is L-BU that is the control wire from the PCM - engine computer . So basically it's saying there is a problem with that circuit !
The ignition system uses individual ignition coil/module assemblies for each cylinder. The engine control module (ECM) controls the individual coils by transmitting timing pulses on the ignition control (IC) circuit of each ignition coil/module to enable a spark event. The ECM monitors each IC circuit for improper voltage levels. Each ignition coil/module has the following circuits:
?€¢
Ignition voltage

?€¢
Ground

?€¢
IC

?€¢
Low reference

But change the coil to a different cylinder an see if the problem moves to that cylinder !
I I

What make , model an year vehicle ? Is it coil on plug ignition system or dis ignition . Did you test for battery voltage at the coil or coils ? Is the powertrain control module controlling the coils ? Does it have a ignition control module ? Automotive Engine Ignition Coil Testing Repair How to test an ignition coil and ignition module with test light

CHECK TO SEE IF IGNITION COILS AND MODULE GETTING BATTERY POWER.IF NOT CHECK THE IGNITION FUSE.IF FUSE OKAY.YOU HAVE FAULTY IGNITION MODULE OR BROKE WIRE TO IGNITION COILS AND IGNITION MODULE..

The Powertrain Control Module or PCM controls all of the ignition duties on this engine. There is no separate ignition module.

Removal Procedure

1. Remove all the electrical connectors at the ignition control module.
2. Note position of spark plug wires for installation
3. Remove the spark plug wires from ignition coils.
4. Remove the screws securing coil assemblies to ignition control module.
5. Disconnect coils from ignition control module. Installation Procedure
   
   1. Install the coils to ignition control module.
   2. Install the screws and tighten to 4-5 Nm (36-44 lb. in.) .
   3. Install the fasteners securing assembly to engine and tighten to 8 Nm (70 lb. in.) .
   4. Install the spark plug wires as noted during removal.
   5. Install the electrical connectors to the ignition control module
6. Hope this Helps !