The radio in my 1992 Lexus es300 doesn't work. I bought another factory radio and hooked it up to the old wires but the radio never turned on. Can anyone tell me what the problem is? I am thinking of buying an after market cd player to put in the car.

Make sure you check for blown fuses. Maybe your previous radio damaged the fuse and that is why the new one does not work either.

Is radio fuse and climate control fuse the same?

I'm not sure on the ES300, check your owners manual to see which fuses control the radio (ACC) with ignition key ON, should be a 10A or 15A fuse and the memory (constant current) +12V at all times should be a 15A or so at it may control other instruments in you car.