I am POA for my father who recently moved to Long Term Care after being to sick to take care of himself in state of Washington which require me to cancel all his apartment obligations and move him to facility which takes state assistance, does he have to pay early termination fees on his internet etc?
There are no special laws in Washington state which relieve a person of contractual obligations in case of disability. You would need to look in e.g. the minimum term addendum if the service is Comcast and you have an obligation to stay with them for some period, to see what your legal obligations are. However, the service provider can waive early termination fees.
Typically, these kinds of contracts don't involve signing anything; agreeing (on the phone) is sufficient. It would not matter whether a person can remember any such terms, the question is whether they could have been aware of them when the agreement was reached. A person's mental state might be such that they are incapable of understanding or consenting, in which case there would not be a contract. I would say that it constitutes a completely separate question (i.e. it would overload this question to add that on), to investigate how the law deals with contracts and people with dementia (whether or not applicable in the instant case).
Setting aside the mental-state question, there is also an open legal question as to what a given customer has agreed to. The benefit of a printed contract to sign is that this question is clearly known. The problem with phone sales is that salesmen do not in fact read out the terms of the contract, and often fail to mention material details, so it may be that a person has not been told of an early termination fee. Some companies have such information available online (my ISP does not), but you can't go from "could theoretically find" to "was given notice". If it's not reasonably knowable that there is such a fee, then the clause might not be enforced. However, it could require a lawsuit (and probably appeals) to establish such case law (if it hasn't been – I don't know of a precedent here). The odds are fairly good that they mailed a (fine-) printed copy of the contract when the service started, maybe along with a lot of advertising, so that the terms of the contract were available.