Need opinion on rescued dog

[Aquattro]

My pitty X was like that, not even aware of people when I got her at 8 months. she'd been in the SPCA for 4 months, banging her head on a concrete wall. I almost thought she was deaf because there was no acknowledgement from her when I spoke to her. No obedience, nothing. Now, a year and a bit later, she's the greatest dog. She plays with toys, tugs on a rope, fetches, etc.
If food doesn't work, you need to figure out what is high value to her. I'd try different foods first, greasy chicken, fried liver, etc. Maybe borrow a neighbours cat and put it on the deck (just kidding).
My border collie was weird like that for a while. We run around th elake a lot, and cross a few small bridges. One day, he gets to a bridge, and skids to a halt. There was no way he was crossing the bridge, so I had to go back and carry him. Maybe carry yours onto the deck, don't put her down unless she's relaxed. You have an exciting challenge, you'll both be happy when you figure out the puzzle