All the lights in the dash was on when engine.

Check the wire that runs to your batterie. That tells the car how much to charge. If it brakes your car will charge way to high, your alternator is fine, that will be why your lights are staying on when the car is running, your looking for a wire that has a plug on it, right on the batterie, + side, Had the very same problem, spent heaps trying to fix the problem, only to find a broken wire