I believe Gnarly has spoken well on this topic -- I, myself, grew up with a CI since the age of 2. I am part of the Deaf community because I understand the frustration and experience of the Deaf -- this, as Gnarly pointed out, ties me in with the Deaf culture. I grew up oral and I was doing well in the hearing world -- but there are times, and it's not rare or seldom, that I encounter ignorant people who disrespect me as an individual just because I either misunderstood or did not hear them. If I hadn't found the Deaf community within reach, I would be overwhelming depressed, because no one else will understand what's it is like in our "world". I feel more comfortable bonding with those who have shared "deaf" experience
ASL is only a tool for us to communciate with each other. Obviously we can not hear each other voices. Does speaking English make the entire hearing community -- no, it does not. Rather it's people's perspective on common sense, traditions, experiences, et cetra.. Also, keep in mind that ASL is not a national sign language. Just like in the hearing world there's English, Spanish, German, Japanese, Chinese... etc etc... There's BSL, AUSLAN, MSL, FSL, etc etc, so that should give a sense of how universal and diverse the Deaf community is.
The Blind, the handicapped are all in their own subculture -- they are not considered part of the Deaf culture because they obviously are able to socialize with others -- people are more courteous towards them because it's a physical disability, and I believe people are more aware of how to be polite toward them. However, Deaf people have a social disability -- and most people would not know we are deaf until they try talking to us - or don't bother once they sense it. We are pretty much barred from the hearing world in some aspects. We encounter hang-ups on relay calls because sometimes they think we are a waste of their time. There are some job discrimination, being passed over for jobs qualified for just because "oh s/he's deaf... can't talk, no way to communicate." Sadly many people still make assumations based on the old "fact" of being deaf and "dumb".
As for senior citizens who are losing their hearing, they are not part of the Deaf community because universally people understand that it's part of the aging process, and are more compassive towards them due to age. And usually elders do deny their hearing loss.
I actually wrote a paper for my Independent Studies for my BA in Anthropology on Deaf culture, and if I still have a copy of it, perhaps you may be intersted in it?