How do you deal with a parent that is unable to communicate?

I can understand how difficult and frustrating it would be to want to help your parent, but not know how. You don't say why your parent can't speak. It could be physical (such as paralysis after a stroke), or emotional (shutting-down and being noncommunicative can be a symptom of depression). Since you say "can't," I'm going to assume the cause is physical.

Has your parent seen a speech therapist? If not, this is where you should start. Ask your parent's doctor for a referral. Speech therapists deal with all kinds of communication problems, including teaching nonverbal communication methods, or referring a patient to a specialist in this area. People who can't talk can often learn to communicate through writing, a computer, hand signals, or by using something called a picture board, where you point to a picture that matches what you're thinking, like a picture of food for "I'm hungry," or a bed for "I'm tired." These methods are sometimes called "augmented communication." Computer technology has led to huge advances in this area. Many non-speaking people find ways of expressing themselves.

Even now, can your parent write you a note; shake his head up & down; use his fingers to point, or to say "yes" (thumbs up), or "no" (thumbs down)? Your parent may need encouragement to try new ways of "talking." It's very difficult to lose communication skills; this is a tremendous loss of independence. Your parent may be on an inward snowball, depressed and closing down. It's possible to reverse this -- it really is! Once your parent learns he can express himself without speech he'll feel much better, and so will you. Start by consulting with a speech therapist. You don't need to figure this out alone; tap into the wealth of expertise in this area.