A senior citizen's car is giving troubles. His son wants to buy a car to donate him right away. Is he exempted to pay the sale tax?

It depends on local sales tax laws in the State. If there is no sales tax on a used vehicle, there probably will be a tax paid when the new owner of the vehicle goes to get the vehicle registered/tags.

Just curious, if the father cannot afford to buy a good used car, how will he afford the car insurance, registration, tags, fuel, maintenance, etc.? One might consider alternate mode of transportation.