Question: "If a person wants to be baptized, but is unable to be immersed into water due to being ill, disabled, elderly...etc. - what should be done?"
Answer: Perhaps the best way to address this question is to start with baptism itself—what it is and what it isn't. Christian baptism, according to the Bible, is the outward testimony of what has occurred inwardly in a believer's life. It is a picture of the believer's identification with the death, burial and resurrection of Jesus Christ. Romans 6:3-4 describes this act as our old sinful selves being buried with Christ and our newly created selves being resurrected to walk with Him in newness of life.
Baptism is not a requirement for salvation, nor does it have any power to save. Rather, it is a symbol of the salvation that has already occurred. We are baptized in order to display to others that fact, which is why many baptisms are accompanied by an oral testimony given by the person being baptized. It is the testimony that is the most important part of the rite, not the rite itself.
While the Bible is clear that immersion is the proper mode of baptism, it nowhere addresses what to do in a situation where a person needs to be baptized but cannot be immersed in water. Some propose baptism by sprinkling or pouring. While sprinkling and pouring do not match what baptism signifies—the death, burial, and resurrection of Jesus Christ—there are clearly some situations where full immersion is impossible. A person who cannot be baptized by immersion should go before a group of believers and publicly declare faith in Jesus Christ alone for salvation, his commitment to Him, and his identification with Him. That would accomplish what baptism signifies.