Yes, get a new car. Yous is probably really messed up inside. If the oil was dry, first you don't know how long it's been that way and second, you should have put WAY more than 1 quart. Like maybe 3 quarts to start with and then see how low it is later. It's a miracle the engine still turns at all and somehow didn't weld itself into a solid block of useless garbage.
This sounds too obvious, I know, but pour about 3 quarts in, start the motor and watch the pressure gauge go up to the normal zone, then shut it off and wait a couple hours, then check under the car for a huge puddle. If you get a puddle, then it's easy to look and see where the oil is coming from. It's even possible that the drain plug is gone.