It sounds as if one of the major components of your Buick’s drivetrain has blown. Let’s rule out the parts that don’t fit you car’s problem. If the universal had failed, it would still try to go into gear as you shifted because the transmission would have been working. It would not have moved, though, because there was no power getting to the wheels. The power was being derailed at the universal joint.The important thing to look for here is the fact that the car would still go into gear and try to move, but would not.
Moving to another component, if either of the half-shafts on the front-drive LeSabre had failed then you would have had at least one of the front wheels trying to move at some point. It would have been pointless because ultimately the broken half-shaft would have compromised the other side and the universal joint.
Still, if the LeSabre is trying to go into gear and one of the front wheels moves, you can rule out the tranny and universal as the problem and have the technician focus on repairing the half-shafts.
Since, there was a loud bang and the Buick stopped moving and still refuses to move, though the engine is turning over, then, it is more than likely a problem with the transmission. Indeed, I would be surprised if the problem was not right at the start of the power transfer chain in the transmission, either the input shaft or the torque converter. Each could fail separately, though the torque converter is the item that would go bang before it stopped functioning. The reason for the noisy failure is that the converter is an energy transmission device as it starts the transmission fluid on its way through the engine. If it fails and there is a build up of inertial energy on the converter vanes, then it is likely it would go bang and then stop.
Since I suspect that the culprit in your problem is the torque converter, I think you can stop your hunt there. It will mean that you will have to drop in a rebuilt transmission into your car’s case because it is just not economic to try to repair the converter. You don’t know the downstream damage its failure might have caused so repairing the individual systems costs just too much. Indeed, if you fix the converter and then find the gearing is gone, you will have to replace the planetary gearing and other packages relating to it. Almost immediately, this puts the cost of your repairs into the astronomic zone.
Yes, $3,200 is a lot to pay to replace the transmission with a rebuilt unit, but it isn’t when you realize that replacing individual systems within the transmission case can quickly raise toe cost to, at a minimum double the cost I mentioned.
I hope I’ve helped a bit. Please let me know what else I can do for you and do tell me the results. I am always excited to hear from readers.