I agree, she may well have been raised by a wild mom cat. If it were me, I would not allow her to hide in the basement. I would set up a room where she can live until she has a little more confidence. Then, during this time, you need to go in and be with her. it may be quite some time before she learns to trust, but as you bribe her with food and try to touch her gently (even if that means laying on the floor and petting her under the bed) she will see that you are friendly.

There are many tricks to making her dependent on you. As you said, shw will come out when she is hungry. So, make sure she knows WHO is supplying that food.

The reards are far from instant, but well worth the wait.

Best of luck with her.

by the way, has she been spayed yet? This would be the perfect time to schedule that and then start the reintroduction of her to your home with access to one small room where she can learn to feel safe.