The transmission oil pump on your Golf GTI is a variable displacement pump that is driven by the engine. The oil pump begins the pressurization of your transmission’s fluid. It provides the pressure needed by the transmission so that it works correctly.
Can you tell me if there is a whining sound the continues whenever your car is in gear and whether it continues as your car goes through the gears and you drive on? If so, then it just confirms the diagnosis is correct.
The pump itself sits at the very front of the transmission at the point where the crankshaft and input shaft meet. It is the torque converter housing. The engine, through the input shaft, provides drive for the transmission oil pump. The oil pump surrounds and is linked to the shaft. As the shaft spins and drives the — for want of a better description — doughnut-like transmission oil pump, the vanes on the outside edge of the disk-like device spin and provide the push needed so that the torque converter will work.
If you note the location of the pump — the diagnosis, if you guessed it, seems correct — you should note something. This won’t be an inexpensive job. The transmission housing has to be opened to access this pump. And, while the pump itself is a rather straightforward affair — a notched disc with a shaft input in the center — getting to it and removing it take time and labor. You are looking at a good eight to 10 hours of work to open and strip down the transmission and another couple of hours on the part and then another good eight hours to close up the transmission. At best, you are looking at two days of labor, possibly more, and part costs. The part will cost, depending on location, between $200 and $400, while the labor, based on a $140 per hour labor rate, will be between $2,240 and $2,800. It’s not an expensive fix.
Might I suggest obtaining a rebuilt transmission for about $3,000. If you do all they have to do is unmount the old transmission and replace it with the rebuilt. It is a lot quicker and, like as not, a lot more reliable. Who knows what other problems will be found with the old transmission open? And, if that is the only problem, it is quite possible that that the now-properly working pump may be too much for the torque converter and may cause another chain of failure.
This may not be what you want to hear, but it is what you are facing.