if only one of the two fans on the radiator are working?

 

No You need to figure out why the fan is not working.

Start the car and turn on the a/c. Both fans should turn on. If not turn off the engine. Unplug the fan that is not working. Start car with the a/c on and see if the electrical connector to the fan has 12V using a volt meter.

If you have 12V, you need a new fan motor. If you don't have 12V, you will have to do some more troubleshooting.

 

And "more troubleshooting" will start with telling us what kind of car we're talking about.

 

98 accord ex

 

To answer the question, no you don't need a new radiator.

You might need something else, fuse, relay, fan motor.

Does the AC work? If so what did the first "test" PA suggested show?