To be clear- you do have film in the camera, yes? Without film, the double exposure mechanism doesn't engage and it will behave as you describe.
With cameras like the Rollei and Yashica, an empty film spool in the takeup chamber will make the camera operate as if there was film (well, you still need film to kick the automat mechanism in a Rolleiflex). But the Autocord, with its top loading and reversed film path, won't be fooled by an empty spool.
There is no roller to put the film between on the autocord.
Anyway- film in camera? Than you have a jammed or broken mechanism inside the wind side. There are small levers that should drop/be pulled into a locked position when the wind action is completed; sounds as if yours is not going into place. If the winding is going ok, sounds as if you can still use the camera but just remember to not wind until after a shot.
The interior of the camera- the levers you need to be concerned with are to the bottom and right of the main wind drum.
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