Title of 1980s novel involving alien messiah, nuclear war, cyborgs and mutations

Question

So this novel I read - It concerned a messianic figure who was constructed here on earth from instructions received via radio from space. Among the details I remember are a police chief who over the course of the book has more and more bits replaced until he is an android. The messianic figure somehow constructs an antigravity drive in the basement of either the Chrysler building or the Empire State Building in NYC, and it eventually takes off during a nuclear conflict, acting as an ark. During the conflict a nuclear device is aimed at the building and bounces off a defensive field, and eventually catches the police android who was held hostage in a ship piloted by a government official, who had a hobby of raising cockroaches and periodically stressing them with pesticides and radiation in an effort to bring about mutations. Any idea what it was? I can't remember the title.

Answer 1

A for Andromeda by Fred Hoyle might match.

A new radio telescope picks up from the constellation of Andromeda a complex series of signals which prove to be a programme for a giant computer. After the computer is built it begins to relay information from Andromeda. Scientists find themselves possessing knowledge previously unknown to mankind, knowledge that could threaten the security of human life itself.

It is a novelization of the 1961 serial of the same name which does include the development of artificial life forms and including a missile attack.

Following Christine's death, the computer outputs a new set of instructions – this time for the creation of a complete human embryo. Fleming is horrified and demands that it be killed. He is ignored. The embryo rapidly grows to maturity; everyone is stunned when it is revealed to be a clone of the deceased Christine. The creature – which they name "Andromeda" – quickly learns to communicate and is brought before the computer. The computer, realising its instructions have been carried out, destroys Cyclops as it has been superseded by Andromeda.

...

Andromeda is put to work developing a program to enable Britain to intercept orbital missiles which a foreign power is firing over British airspace as a demonstration of power. Using the missiles designed by Andromeda, they are successful in destroying one of the missiles. The Government is now determined to make full use of Andromeda, not just for defence but also to aid industry. Fleming continues to make trouble and has his access to the computer revoked. He is horrified to discover that the Government has made a trade deal with Kaufmann and Intel for the rights to a new enzyme that Andromeda has developed that heals injured cells. By this stage, Dawnay is also beginning to have doubts about Andromeda – she agrees to aid Fleming by entering a program into the computer to convince it Andromeda is dead. The program is quickly discovered and reversed by Andromeda. However, the computer soon exacts its revenge – it corrupts the formula for the enzyme, making Dawnay and her assistants sick.