If anything is running, the controls to move the servo or winch must be getting a signal to tell them to move, or they are both faulty. Servo testers are amazingly cheap if you are prepared for a bit of a wait for delivery, still good value locally, and they sort out a lot of questions in one step.
Having said that, it is common for servos and winches (which are really just servos with a bit of rearranging) to give a twitch on powering up. If the correct procedure (TX on first, Rx on last) is followed, it might be that the servo and winch are just taking up the positions that the transmitter is telling them to go to. More information on the general type of radio and nature of the "running" would help the guesswork.