In my 96 vw jetta there is a loud vibrating noise under the center console everytime i give it gas .

the car should still be under warranty from time and mileage so have the problem checked by a service section under warranty
vibration could be from failing cv joints, misfire and any number of other things the loud exhaust may be a failed flexible section on the end of the manifold before the cat converter.

check that a valve rocker has not jumped off a valve end and is pressing down on the valve spring retainer.

Factory stereo system?

I have a 96 jetta What type of noise ? Could it be the solenoid on the starter ?

Don't go on the 400 highways!
Tire noise?

engine mounts

The cam shaft sensor operates the speed and spark of the engine without it work properly the car will shake and will not run good. It will run rough and will hesitate and may even cause more damage if continued to operate in this state. Cam sensors are not expensive anyhow anywher from $50 to $150 good luck

underinflated tires, wheels out of balance or wheel alignment. Heater blower motor bad and/or going bad

I had the same problem with my 96 jetta trek edition, solenoid was engaging but the trunk was jammed, went in via back seat, fold down the seat and crawled into the trunk unscrewed the latch, cleaned and greased the latch mechanism and hinges, then screwed latch back, no problem since. The fusebox is underneath the dashboard, if the fuse is good, test the solenoid to see if it is working correctly, be careful have an expert in electricity do the testing for you, if solenoid is good, might be your switch in your console, if the switch is good, might be mechanical, these are basic troubleshooting procedures.