99 vw passat, when running, MIL lite, on car vibrates- shakes

No flashing light and rough shaking will be part of spark plug but also a very bad miss fire. I am going to guess that your engine is a 1.8t if so you have 4 coils that sit on top of your spark plugs that most likely are arcing you will need to figure out which coil is failing or you can save yourself the trouble and replace all 4 and the spark plugs. before you do that though check your wireing going to your coils look for broken wires or the ground that is next to the #1 coil that is the one closest to the front of the motor and you. hope that helps. that will be the start to fixing your issue also when you pull out the spark plug look down the hole first and make sure that there is not oil in the bottom of the hole if that is the case you will need a valve cover gasket as well. good luck hope that helps