I'd like to know why he was denied his LPR status. I'd like to know what portion of the case was denied; the I-130, the I-485 (if it was while he was here) or if he was denied at the consulate. This will help define the issue.
I agree that we would need more information to be able to help you with this issue. Waivers of inadmissibility are complicated legal matters. Your father probably got something in writing explaining why he was denied his immigrant visa. You should take a copy of that paper to an attorney to review. Depending on why your father was denied, it is possible that he might be eligible for a waiver. However, different categories of inadmissibility have different requirements for obtaining a waiver, which is why I highly suggest you see an experienced immigration law attorney about this matter. I am very sorry for your situation, and truly hope that you and your father are able to find the resolution you seek. Please feel free to contact me should you have any questions. I speak fluent Spanish.
Amanda M. Diaz
Sorry to hear about the difficult situation your family must be going through. it would be difficult to answer your question without knowing the basis for your father's denial - whether it was the visa, the adjustment. I would suggest having an attorney review your paperwork thus far and then you can be given an informed opinion about your father's chances.
Samuel Ouya Maina, Esq. 415.391.6612 email@example.com Law Offices of S. Ouya Maina, PC 332 Pine Street, Suite 707 San Francisco, CA 94104