In terms of physical issues, you could ultrasound the hind suspensories if you haven’t already. Bilateral lesions can manifest as not wanting to go forwards. Kissing spines/cervical spine spurs could also result in random explosive behavior.
In terms of behavioral issues, will she go forwards on the longe? Will she go forwards on a completely loose rein? If yes, maybe she’s feeling “choked” when ridden into contact, or the problem is with some part of her that’s required for collection (back, hind end).
If you’re confident it’s mostly behavioral, I second (third?) teaching her to disengage her hindquarters. It’s a safe and effective way to make them move their feet in a position where it’s very difficult for them to rear/buck/run off.
If no luck, get her re-started by someone good. The point of starting them isn’t just to get them to trot/canter etc, it’s to get them happy to respond to small, light cues. If an otherwise sound, comfortable horse feels that the best option when presented with a cue is to ignore you, or to wait until you yell/scream/beat them with a longe-whip before they respond, then the starting process has failed, and you need to go back to basics.