Just bot a 2004 Tiburon GT - Manual with 124k miles. It has several issues. 1. needs some major shock/suspension work - the car has that real bad bouncing feeling rattling sound 2, transmission - can not get it into 2nd gear at all it just grinds and reverse is really hard to find. Other then that the engine seemed to have plenty of power in all of other gears and all of the rattling seemed to be related to shock/suspension issue. It was my intention to get it to a mechanic to have it looked over and fixed. Tonight when I came home I was trying to back into driveway, it died and lights were really dim. we attempted to jump the car - lights got brighter, but it still would not start didnt even turnover. I went out a few hours later and the lights would not even work. the only thing that i did notice when we attempted to jump the car was a low buzzing noise when the key was turned coming from the left side of the engine compartment closest to the windshield - passenger side....other then jumping the car, we have not done anything to fix it

Bad struts may cause a bouncy ride but control arms (or more likely the bushings in them) can cause some drivability problems. The control arms usually have the bushings pressed in and the whole piece gets replaced. Seems like a lot of suspension work for a car under 100k. I would get a second opinion on the severity of the issue.

F39
121 OHM Resistor
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Electronic Suspension Control (ESC) Module

Electronic Suspension Control Description
The electronic suspension control system, also known as the magneto-rheological real time damping (MRRTD) system independently controls the fluid viscosity in each of the 4 shock absorbers in order to control the vehicle ride characteristics. The electronic suspension control (ESC) system is capable of making these changes within milliseconds. The ESC system consists of the following major components:
• The electronic suspension (ESC) module
• The front/rear position sensors
• The front/rear adjustable shock absorbers
• The shock absorber electrical actuators, which are integrated within the shock absorbers
The ESC controls the damping mode selection according to the following factors:
• The vehicle speed
• The chassis pitch input
• The steering position
• The body to wheel displacement
The ESC module evaluates these inputs in order to separately control the shock absorbers, providing an enhanced ride and comfort level over the widest possible range of operating conditions.

It's a terminating resistor for the GMLAN serial data network , also has one in side the ECM - engine computer > Do you know anything about C.A.N. - controller area network ? All the modules on the vehicle are hooked to the data bus . They share info. between modules on the bus.

Circuit Description
The communication among control modules is performed primarily through the GMLAN high speed serial data circuit and the GMLAN low speed serial data circuits. The modules that need real time communication are attached to the high speed GMLAN network. The body control module (BCM) is the serial data gateway between the networks. The purpose of the gateway is to translate serial data messages between the GMLAN high speed buss and the GMLAN low speed buss. The Local Interconnect Network (LIN) is another serial data communication network used on this vehicle which is dedicated to the door/power windows subsystem. Below are more detailed descriptions of the individual networks. The gateway will interact with each network according to that network's transmission protocol. Refer to Body Control System Description and Operation for more information about the gateway.

Videos on youtube explain how C.A.N works
https://www.youtube.com/watch?v=OdTFRX5KxZw&t=192s

Your air shocks are not working
you should have an air pump in the back end of your car which pumps the shocks up but the pump may be worn out as well the air lines may have holes in them. If the pump is working you will hear a humming as the pump works.
My pump was shot and my shocks were worn out so I replaced them with manual air shocks you pump up with an air compressor with the hose coming out under my bumper out of sight. I check them every six months and top them up. Sure cheaper than buying the pump and all the trimmings.

• The magnetic ride control system senses speed and oscillation of suspension and adjusts shock dampening for a comfortable ride. If a shock is bad or the suspension sensors are damaged in anyway the system deactivates and does to a default setting, and the warning comes on. Did you hit any real bad potholes? or probably just wear and tear.. You need to have your suspension system checked.. shocks, control arms, alignment, etc.

It is probably a combination of several of the following:
1. tires out of balance and/or out of round, cupped, bulging etc
2. bad shocks
3. loose suspension bushings front and/or back
4. bent or out of balance drive shaft
5. bad U joints
6. bad wheel bearings

If they were as old as the transmission, they were probably of minimal strength; reinstalling the transmission and re-setting the car's weight back on the suspension may have taken the last oomph out of your shocks. The rebuild must have been awesome, get some new shocks and make it a real new ride!

All systems? or just a few? You can go to http://www.hmaservice.com/ and register your vehicle (by VIN). Afterward, you'll have access to the ETM (Electrical Troubleshooting Manual) and Shop Manuals as well as Service bulletins.

your shocks dampen the movement and up and down flow or you suspension. it is may be a bad coil spring

i would check your front struts. when your struts are bad your car will tend to pitch and roll a lot more, and even something as simple as turning a corner can activate the stabilization function. also check the recalls for the cts. there is one out there that affects the front suspension that could have a bearing on your problem.