Jasjas, welcome to the forum. I am sorry to hear that your dad is so sick.
First of all, has he stopped drinking? It's crucial that he stop all alcohol intake. What type of disability has he applied for? SSI or SSD? SSI is for people who don't have enough work history to qualify for regular Social Security Disability. People on SSI should get Medicaid immediately, unless he has too many assets. If it's SSD that he applied for, he has to wait 2 yrs. from the time he applied to get Medicare. Usually, when one applies for SSD, they will automatically evaluate for SSI and Medicaid, as well.
Is there a teaching hospital near your dad, or a clinic he could go to? Those places will generally take people without insurance.
You asked about transplant. Your dad would have to have documented sobriety in AA or alcohol counseling for 6 months before he would even be evaluated for a transplant.
Are you in the same city as your dad?
If you read some of the other posts, especially regarding alcoholic liver disease, as well as the Hepatitis Resources folder at the top of the page, you will find a lot of information.