Father unable to complete FAFSA, any advice for loans?

Hi, I am at a loss here so would love any help.

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My little sister is a sophomore at a relatively inexpensive state school, and my parents are not contributing financially. Her first year my grandmother paid for her schooling, which we are really appreciative of, but after the first year she was unable to contribute any more. My sister managed to attend this past fall semester, due to a combination of savings and moving in with a family friend to cover costs. However, she is trying to apply for loans for the spring semester and we are having a really hard time with the FAFSA, because my father can/will not fill out his part.

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My father has a neurodegenerative brain disorder with physical and mental symptoms and he has not been able to work in a year due to this. He also didn't file his taxes for two years before that, so we are unable to complete his portion of the FAFSA. Even if he had done his taxes, it is extremely difficult for him to focus/complete tasks, so him being capable of completing the form is doubtful. My sister's college basically told us that unless my father is dead or in prison, his portion of the application is necessary to submit. If we can't submit the FAFSA, my sister cannot apply for loans, right? No one in my immediate family is eligible to co-sign for my sister on private loans.

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What are our options here? Is there a way to officially exclude my father from the FAFSA? Can my sister get any loans without a co-signer AND the FAFSA? We're freaking out, because the deadline to enroll is coming closer and closer. My sister is a really smart kid, and she works two jobs to support herself so I really don't want to see her drop out. Any advice would be welcome.