first gear

The following test is very dangerous. Do not try this if you are going to let the brake go at anytime. YOU MUST HOLD THE BRAKE DOWN WITH YOUR LEFT FOOT 100% OF THE TIME.

OK. Open the hood and turn on the car. Have an assistant stand to the SIDE OF THE ENGINE NOT IN FRONT OF THE CAR. Next, put your foot firmly on the brake with one foot and your second foot on the gas simultaneaouly. Put in gear iff the brake is all the way down. now torque the motor by slowly giving it gas, while you brake NEVER IS UNDONE. Your assitant is looking at you engine to see if it is moving forward and backward erratically. Now torque in reverse gear.

Hold the brake 100% of the time. With the seond foot torque (giving gas) in reverse. You assistant is looking to see if the engine moves erratically.

It sounds like you have a broken engine mount. If a Toyota, there is a "dogbone" looking mount on top of the engine in front of the passenger in the engine compartment. Notice it does not happen when you run lightly, but it noisey when torqued.