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Hello, so far it sounds like the contacts in the contactor are fused (burned closed)... the solution is to replace the contractor, but in doing so it is *crucial that you do not get the 24 volt control coil wire confused with the 230 volts and wire it incorrectly, that would burn out your entire controls system.
Tell me if you want coaching on doing that yourself, or if you want to call in an HVAC repair outfit to do it for you. We can go from there.