I know, and here, with the social context, enter inevitably value judgements.
We need to further specify. In my understanding people who can speak (even in a "challenged" way) are always conscious. The question is the ethical side: are they to be considered ethical agents like other adults? Weaseling out here would be to say that every case should be judged uniquely, there are no two the same persons, yadda yadda. Philosophy deals with universals, so that would be too cheap.
Let me put it like this: they, just like everybody else, should be considered adults. Let's say such a person is charged with killing another fellow human being. At the beginning of the trial he should be immediately put to decide: "Regardless if you plea guilty or not guilty, do you understand yourself to be an adult, completely responsible for his deeds?"
If he says yes, the trial must continue normally, if he says no, he performatively abandons his claim to the same ethical status we treat others with.
With regards to euthanasia: I believe that anyone, regardless of their reasons should be given the opportunity, including the mentally handicapped.
You are talking about people who are near- or completely vegetative, non-speaking, can't feed themselves, defecate uncontrollably, etc. Their very consciousness comes into question. The tricky bit: are they electo-mutists? Do they have an inner monologue just like everyone else, fantasies, hopes, etc. but being unable or choosing not to express them?
The general problem is of representation. They can't represent themselves, so inevitably somebody comes to do this for them (and with this inevitably misrepresent them). Let's say a family member comes forth: she just knows that Mr. Carrot is suffering immensely, this is not a real life, etc. and should be euthanized. Do we have medical evidence of his suffering? If so, euthanasia seems humane. If not, society should take care of him until he dies naturally unless his caregivers from their own judgement conclude that he should be euthanized regardless. For this they would need to come forth and present their case: we know that he is not suffering in a medical sense, but…
When you go into legal, political, etc. context value judgments inevitably come up.
When I said that a dog is a sentient being incapable of becoming conscious I believe I stated a fact. Same with the newborn kid, the 3 year old, the adult. These aren't my value judgments. Well, they could be, but I thought we agreed that these were facts. If we still agree that these are facts, it entails that these qualitative differences are "objectively there" and my later value judgments (in legal context, for instance) only reflect on these objective differences.