I’m going to second all of the folks that have said to run the Net Price Calculator (NPC), but you may also want to ask schools with generous financial aid about a professional judgment pre-read with respect to the disabled parent. (This means that after you run the NPC, you would ask a financial aid counselor at the school to review your family’s information because of the disabled parent and see how that would change the school’s assessment of your financial need.)
If your parents do not want you to know their financial details, you do not need to be present for them to run it. Rather than MIT, I would suggest running Princeton’s NPC as it is often considered the most financially generous college in determining need. If that NPC (and a professional review afterwards) does not come back as affordable, then it is unlikely that any school will provide sufficient need-based aid, in which case you know that the necessary path to affordability will come through merit aid and lower cost schools.
Additionally, depending on your parent’s disability status, you may be eligible for financial assistance due to that disability. As an example, veterans that are disabled due to activities from their service will often have their dependents qualify for additional aid. I would investigate any options through that route as well.