My 97 lexus sc300 started making whining sounds a few weeks ago .

OK! Here is what you are going to have to do about your car.power steering problem. How do i know?? Trust me, my 1999 SC300 did the same thing last week. Remove the power steering pump from the car. Remove the PS resevoir and drain it of the old fluids. Then look very closely into the resevoir and look to see if there is what appears to be a small piece of screen in the bottom of it. this screen is attached to the inside of the resevoir to filter out any larger pieces of debris that may be introduced into the system. If you will notice, with the help of good flashlight ,check at the bottom of the resevoir you will see the pump feed hole. This screen/filter has been detached from it's mounting and has been sucked down into the pump feed hole. Remove the screen section that has broken loose and trash it. This screen is stopping up pump feed causing your power steering problems. Good luck bud!! Hope this helps out

Check to make sure there power streering fuild in da pump,and check hoses for leaks.