Q: My car hates me.

It sounds like you may have a couple of different issues. The problem with the shaking in the steering may be related to the steering system. What you are describing sounds like a problem with the rack and pinion gears. The rack and pinion gear set does two things: It converts the rotational motion of the steering wheel into the linear motion needed to turn the wheels. It also provides a gear reduction, making it easier to turn the wheels by the use of reduction gears where the steering shaft connects. This system uses a torsion bar driven valve to direct and relieve pressure in a cylinder. When the steering wheel is not being turned, the steering valve is at rest. In this position fluid flows around the valve and out to the reservoir which is where the power steering fluid resides when not at work. Slight pressure also enters both sides of the assist cylinder. Because pressure is equal on both sides of the piston nothing occurs when the wheel is straight ad no assistance is need to turn the wheels either way. Occasionally you’ll notice that your steering wheel will make jerking movements or sudden turns to the left or right when not directed by you. This is typically the sign of loose bearings in the steering rack and the result of the steering rack literally moving without input.

The issue with the vehicle not starting may be related to a faulty starter relay. The starter relay directs power from the battery to the starter solenoid which then engages the starter when you turn the key. When this is not working properly, you may notice intermittent starting problems including no response when turning the key to start. Generally, when this does fail, it does so very randomly and usually without warning other than intermittent starting. The power from the battery will still power other accessories such as radio, horn, etc., but you may not have any power to the starter. I would recommend having an expert from YourMechanic come to your location to diagnose and inspect your vehicle.