VA's "lemon law" does apply to used vehicles, but only those that you buy from a dealer that are still covered by the original manufacturer's warranty. It does not cover other used car sales. Since you bought a 1996 car, it is no longer under the original manufacturer's warranty, so the lemon law won't help you here.
If the dealer did not offer its own warranty on the car, you may be out-of-luck here. Used car sales are "as is" and thus the buyer takes the risk of any defects in the car when buying it. For this reason, especially with an older car like that, it is a good idea to have an indepedent mechanic inspect the car for problems before you agree to buy it.
There is, however, a potential remedy for you if the dealer misrepresented the condition of the car to you.