So I was parked on a hill yesterday, with the front of the car facing down the hill. Car was in park with ebrake engaged. I started the car, put my foot on the brake,put it in drive , released the hand brake then let off the foot brake to start rolling on down the hill. The car didn't move what so ever with no brake at all engaged. Then I tapped the gas and it clunked into gear and started driving perfectly fine. Then I put the car in to reverse in the same spot on the hill and it would clunk into reverse every time I would give it gas. Is this a transmission issue or a differential issue? The transmission is great and shifts amazing. The car only has 146000 miles on it and I can't imagine the transmission slipping and even if it was I wouldn't sit still while in drive facing downward on a hill. Maybe a diff issue? someone please help I've asked a couple mechanics but they didn't seem to help.

You may have already checked this but I had very similar problem in 740 auto when I put it in drive and went to accelerate nothing really happened for a second then it would clunk into drive and go fine. I was low on ATF so I put some in to spec and it was fine. FWIW...

U-joints?

You may have two issues. First. The Brake Calipers might be dragging ever so slightly which caused the 'No Roll, when you released the Brakes.

The clunk: If it's not all related, I would look at your Torque Rod bushings.
Torque rods hold your rear axles from Rolling. If the Bushings are worn, then the axle would rotate a bit when put in gear and accelerating... The axle rotates a bit and then Clunk against the spacious open hole in the Torque rod.
Do you know where to look for the Torque Rods?
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'75 Jeep CJ5 345Hp ChevyPwrd, two motorcycles, '85 Pickup: The '89 Volvo is the newest vehicle I own. it wasn't Volvos safety , it was Longevity that sold me http://home.lyse.net/brox/TonyPage4.html http://cleanflametrap.com/tony/

How about parking your car in the same place and in the same manner.

Then start the car, put it in neutral, then release the parking brake - and see what happens.

Even if you have a problem with various things, the car should roll forward.

Another thing you can try is to drive at a slow speed and stop the car with the emergency brake - hold the button in when you do this - once again the car should roll forward when you release the emergency brake.

Have you read the 700/900 FAQ? - your brakes are similar or identical to those cars.

Are all your rotors clean and shiny?

I'm wondering if this is being caused by the 240's characteristic small amount of wind up in the rear suspension. When parking on the slightest slope, up or down, the car will roll an inch or two after the handbrake has been applied. Noting that I have a manual, I wonder if this movement turns the prop enough to load the gears in the autobox if the lever has already been put into park and has the locking pawl engaged. This extra amount of locking would have to sort itself out when you put it in gear. That might be the clunk. As you say it doesn't happen if you park on the flat this might be the case. You could try holding it on the brake after you have parked, GB in park and hand brake on as usual and then put the lever into drive and then back into park. Experimental but do it safely.

Do very very rarely use the e-brake or do you use it regularly?
Wondering if maybe the e-brake cables are a bit frozen and a little help from accelerating released them.

sloppy U joints do clunk but would not cause a car to stand still on a hill.
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'75 Jeep CJ5 345Hp ChevyPwrd, two motorcycles, '85 Pickup: The '89 Volvo is the newest vehicle I own. it wasn't Volvos safety , it was Longevity that sold me http://home.lyse.net/brox/TonyPage4.html http://cleanflametrap.com/tony/

I just bought the car less then a month ago but I usually always use the ebrake on all my cars to take some weight off of the transmission. But I was thinking the same exact thing but when I was in reverse it would clunk every time the car would stop and I would give it gas. Given I usually give it a little gas before releasing the brake completely to prevent from rolling forward. But it only did it on the hill and never on flat ground

Start with your transmission and engine mounts. If bad, they can cause the clunking and shift delay. If they have never been replaced they are overdue because of age (29 years!) not mileage. Rubber mounts deteriorate over time.

A bad driveshaft u-joint can also cause clunking.