The cooling fan doesn't kick on until the needle is a good bit past halfway...if you look on the passenger side under the hood, near the shock tower right in front of your PCM, there's two electrical connectors. The one closer to the shock tower contains the wiring for your cooling fans (this is assuming your car is the same as mine, which is a 96 3800). There is a blue wire and a green wire on the top row of the connector - One controls low speed and one controls high speed on the fans. If you strip a little bit of the wire away and ground the wire, the fan should come on, even if the car isn't running.

Assuming your fans turn on, that means your wiring, relays, motors, etc are all working. If they don't turn on, you know you have a wiring or relay issue (since you already tested the fan motors). If the fans absolutely do not turn on automatically despite how hot the motor gets, you might have a bad PCM.

You could wire up a switch to turn on the fans manually (just by grounding the wires I mentioned above) or get a relay to connect the wires to ground when your ignition is turned on. Just be warned that this might set off your CEL.