2004 Pontiac Grand Prix car shakes

Could use a lot more detail than that. Stop on a slight incline, release the brakes, and see if the car creeps downhill on its own. If not, the brakes could indeed be sticking and that will cause a pulsation in the brake pedal and a shimmy in the steering wheel. GM hasn't had much trouble with sticking brake calipers, so my first suspicion would be contaminated brake fluid. Any chance the slightest hint of a petroleum product got in the fluid? That could include engine oil, power steering fluid, transmission fluid, or axle grease. Check if the rubber bladder seal under the reservoir cap is blown up and mushy.