Both my aunt and I really appreciate the suggestions offered so far, and I am interested if anyone else has any experience with a similar situation or has additional suggestions. Both myself and my aunt have taken pictures of the damage as well as the broken roofing material strewn over the yard. A claim has been filed with homeowners' insurance and an adjuster should be coming out soon. Interaction with the company is being documented. The company still has not returned phone calls (big surprise
Since the company is still in business, presumably still carries liability insurance of their own, AND the warranties are still in effect per the job contract, I don't understand why my aunt would have to pay anything out of pocket (except for the deductible if homeowners covers the damages) I understand dealing with a situation like this is a hassle, and I'm helping her as much as possible, but I can't see how she should be on the hook for any of this.
Another question: If this is covered by homeowners' insurance, would my aunt's policy cover the damage, then go after the company and/or their insurance for reimbursement? Like the Subrogation example that Wuzzat cited.