04 Audi A8L 3.0 Car jerks when I press hard on the accelerator.
 

Well, I would like to enlighten you guys on some history on my car. I live in Singapore so the driver seat is on the right side and mileage is calculated in KM. I drive an 04 Audi A8L 3.0L V6, right driver seat, mileage ~140,000KM (86,600MILES). I am not really a car expert...

Back around in April I allowed my friend to drive my car and he pretty much caused a gearbox failure, in which I cannot start the engine at all (I think he probably shifted the Gearstick into the "P" position before the car fully stopped but he still denies this till today), anyway the gearbox was replaced at the local workshop (which costed a bomb) and shortly after my engine suffered from some overheating issues, (making alot of noise) and upon inspection, it appeared that the fluid had escaped and the cap of the coolant bottle was loose (so probably my engine had suffered some damage as of that).

Anyhow after fixing all these problems and the damage that my car has gone through, a small problem has emerged, in that the car jerks whenever
1. I press the accelerator hard
2. When the car is moving around ~20KM/H (12MILES/H) and I move the Gearstick to the "N" position
so far I have avoided doing these 2 things so as not to exert any more stress on my car.

Additional things that I have noticed :
- When I accelerate from 0km/h, I have to lightly step on the accelerator initially. As the car speeds up, only then can I slowly increase the strength that I step on the accelerator, so as to avoid any jerking of the car
- So basically the car jerks when there it experiences a large ACCELERATION of speed
- I can still reach high speeds on the highway without any problems with the car jerking. So far the fastest I have dared to go is 140KM/H (86MILES/H)
- When the car is stationary, the car does not jerk when I move the gear stick to the "N" position while the engine is on. Apparently it only jerks when the car is moving, and I push the gearstick to the "N" position.

I am deeply grateful of anyone who might have any advice, or have previously experienced a similar problem and got it fixed by replacing a particular part or two. I am only willing to spend up to 2,000 as I am looking to get a new car next year or the year after. I am also aware of being able to purchase parts from ebay or have them repaired/remanufactured. So these are options that I am looking for if anyone could shed some light on the part that needs to be replaced!!!
Thanks so much in advance and thank you for reading my lengthy post , I just wanted to be precise so that you can understand my situation fully.

Regards,
Shawn Ng.