Raul, the Vertibird mechanic, has the motivator that K-9 needs to get back to operative mode. Dr. Schreber removed K-9's ability to move when, during the experiments, K-9 disapproved of the doctor's sadistic methods and bit him. This information can be obtained from Cookie (the base cook), the doctor, or K-9 itself. One of the lockers in the Vertibird hangar contains the required motor.
If you tell Quincy in the northeast hangar that Raul sent you for the plans, there will be a dialogue option for you to tell Raul that Quincy wants to see him, whereupon he walks off to beat him up, leaving you free to retrieve the K-9 motivator.
After getting the motivator, Dr. Schreber must be killed. He is on subfloor 1 of Navarro. The laboratory room is soundproof, so you can close the door and kill the sadistic doctor. Now you can talk with the cybernetic dog, and use the part on it to get it fully functional.