SONY KV32XBR400 (year 2000) screen is blank when power turned on

The clicking you are hearing was probably always there, it's just that when something goes awry, one pays closer attention. What you hear is probably a relay that connects power to the rest of the set. Since our sets can respond to a remote, they always have a little bit of life to supply power to the infra-red receiver so it can respond when 'off.'
I see two possibilities; the relay itself has burned contacts and not always 'closing' as it should, or, the high voltage circuit is failing to turn on as it should causing an excessive current to flow for a moment and a protective circuit to trip and disconnect the power from the main supply.
It probably will get worse if the problem is not found and could damage other circuitry as well.
Good luck finding a TV repair man who isn't deceased or out of business but I do recommend you try to have it repaired. Once repaired, it will outlast most any panel/flat screen-type TV as it appears nearly all of them are failing much too early in life.
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