I assume that you are familiar with the procedure to get automatic hubs engaged and disengaged. So at least one may be bad. Have you tried jacking it up after engaging 4x4 and checking to see one or both are not engaged? Jack one side up so the wheel is off the ground and turn the drive shaft by hand, if the wheel turns it is OK. Then repeat the procedure on the other side. On an open differential, (stock on a Bronco), the power goes to the free wheel, so if one fails to turn while of the ground that hub is not engaged.
Then you can either fix th e problem or convert to manual hubs.
Please only post a problem in one forum. I have deleted your duplicate post in the general Bronco forum.
Good luck,
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