Car shuts off when transmission is shifted into R or D, codes P0755, P0760 and P0765

Hello, there is a technical service bulletin on this issue. The reason the vehicle is shutting down, I believe is it's going into failsafe mode. Considering codes for solenoids that are located inside the transaxle very close to each other, it sounds like you may have a wiring issue affecting all 3 solenoids. The bulletin refers to a short to ground inside the transaxle. The transaxle oil pan must be dropped to inspect the wiring harness inside. It's highly doubtful that all 3 solenoids went bad at once. So depending on how comfortable you are in taking the pan down to check the harness. To start with you might try just checking the wiring going into the transaxle, like the harness plug on the transaxle for damages. But the bulletin refers to the inside wiring being the issue. There is an arrow pointing to the spot to be inspected on the diagram below. If the vehicle is still under warranty which unfortunately I doubt due to its age, but you do have low mileage. But inspect all the wiring around the transaxle and that area before taking the transaxle apart. Since it is a technical service bulletin, the dealership may be required to repair this problem. I hope they do for you really.

Let us know what you find, I'm interested in this issue. It will help others in the future as well.

Well, at least the service bulletin lead you in the right direction, hopefully it didn't cost you too much to fix.