Radiator fan motor not working?

Okay, so you tried going directly to the battery with the fan wiring and it made a strange sound but didn't turn. Sounds like the motor failed internally. Sounds like you know the testing process. This is the wiring for that if it's a US vehicle.

HMM, the image didn't make it through. There are 2 fuses in the fuse box at the battery. They protect the relays and the fan motors. Then there are the relays that control the fan motors. This system works by using the three relays together to regulate the fan speeds. In the "low" speed the relays run the power in a loop through both fans so that they are in series and run on about half the battery voltage. Then if the engine keeps getting warm the ECM triggers the third relay to toggle it and now both fans are getting the full battery voltage. They work by changing the ground path through the motors. So, in "low" the power comes from both fuses to the relays, however relay 1 is the only relay that turns on. That sends power from the relay through the Blue red wire to motor #1, then it comes out of the motor on the Blue yellow wire to relay 3 which is "off" and it passes the power through into the Blue wire that goes to fan motor #2 and finds the ground through that motor on the Black wire. In that mode having a bad relay or motor in either location would stop the fans from turning. Now the engine starts to get hot and needs more cooling, the ECM now turns on all 3 relays. That now sends the power from relay 1 to fan 1 as normal, but with relay #3 now on the power is sent directly to the black wire and ground. That gives fan on1 full battery voltage, and it turns faster. Also now, because relay #2 is now on it sends power through the blue wire directly to fan motor #2 and it now gets full battery voltage and runs at high speed. A quick test that generally works is to unplug the engine coolant temp sensor. This tricks the ECM, so it turns on both fans on high to protect the engine from overheating.
Or you can pull the relays and test the circuits by jumping relay terminals. If you use a test light to check the fuses and have power on both, then you pull the relays out of the relay box. You should find power on relays 1 and 2 at the #1 terminal in the socket. If the key is on you should also find power fed to the relays from the main relay on terminal #3 of each socket. That is the power for the relay coil. The ECM then supplies a ground through the individual red wires to turn the relays on as needed. So, you should find power on terminal 3 in all three relay sockets. And power on terminal 1 in sockets 1 and 2. To test the wiring the easy way, take a jumper wire connected to battery positive and use it in the relay sockets. When you touch it to terminal 2 in relay two, one of the fan motors should come on. That would show that the power circuit from that relay is good, and the ground for both fans is good (they share the ground circuit). Now to test the other circuit put a relay back into socket #3 and apply power to terminal 2 in relay socket #1. If the wiring and fan motor is good, you should now see both fans on but at a lower speed as they make the low-speed circuit. If they don't turn it on, then it's likely a bad motor. For replacement you would need to replace the cooling fan motor(s). As the dealer network no longer exists you might find the parts online. There are two different motors. As you look at the fan assembly there are a left and a right motor. The left motor is part #1712065J10 and the right motor is part #1712065J00.

(Your short finder will point at the fan motors because they are essentially a piece of wire wrapped around the core and then going to a ground point, so they look like a shorted wire).

Just to be sure. With the key on you should have power to pins 3&1 on relay 1 (control and main fuse) On relay 2 you should also have power on pins 3&1 (control and fused) then on relay 3 you would have power only on pin 3 (control only) If those are what you found then the power side is good. Fan 1 should power on if you apply positive power to terminal 2 in relay 1 socket and ground to terminal 1 in relay 3 socket. Then fan 2 should come on if you apply power to terminal2 in socket 2 or terminal 4 in socket 3. Just want to verify that.
If neither motor powers up Verify the ground to the motors. Wouldn't want you to spend money only to discover the ground was bad. Another thing, connect up a test light in place of each fan and see if they come on while testing. If they work but no fan then you have bad motors. Parts wise look on RockAuto. Com They show 5 brands from 120-250 dollars for complete assemblies. SKP SK621509, DORMAN 621509, CONTINENTAL FA72653, UAC FA50510C and TECHPRO SZ3115107. I'd probably opt for the UAC, I've used that brand before.

The relay block you want should have 4 relays in it in a line. The relay with the fuse next to it you disregard. Then the relays should be labelled in the sockets they plug into as E29 E30 and E31 They are the relays and should be 29= 1, 30= 2, 31= 3. The relays themselves will look like the picture and have 4 or 5 terminals with internal wiring as shown. For the relay internal wiring diagram the ABCDE translate to the external terminals as - A and B would be 3 and 5. C will be 1, D will be 2 and E will be 4. Now one thing to remember is that the coil can be connected either way, that is because you are viewing the relay upside down, so in the socket with 5 terminals there will be 3 one direction and 2 at a right angle. The three will be A - E4 - B the two terminals at 90 degrees will be D2 - C1 (C on the end), A can be either 3 or 5 depending on which one they wired as power and B is the same.
Did that help at all. It's one of those things that I can look at and understand but describing it is different because there are about 4 different ways that they describe the terminals.
For instance some relays will be labelled as the coil as 85 and 86, then the terminals as 87 and 30 with 87A as the normally closed. The last image is looking into the relay socket.

Funny you mention that, Not a doctor but do have 25 years as a FF/EMT myself. Rode the bus for many years.

We will be here. No rush.

It sounds like you have a couple of bad motors. One item to try, Connect a test light in place of each fan ( they run in series in low and parallel in high, if you don't have a good circuit in both motors it stops both of them from working. You don't have access to a bi-directional scan tool do you? With that you could likely turn the fans on and off easily. However I'm not sure which ones would cover that vehicle very well, even though they show coverage.

The grounds on the fans are somewhat deceptive because of the way the system operates. There are the two motors in the fan shroud. In low speed operation the power goes into one motors positive lead, then out of the negative lead and into the second motors positive lead. Then through that motor to ground. That way you end up with effectively one half of the battery voltage going through each motor. So they spin slower. Then when the temperature calls for higher fan speed the relays engage and it now treats them as two individual motors by splitting the ground. Now instead of two motors in series each one is fed full battery voltage and you het high speed operation.
The catch to this system is that a failure of the ground or either motor leaves you with no fan operation. You said you tried connecting them directly back in your post and that the fan made strange noises but didn't work. To me that sounds like at least one of them failed. That alone would stop them from operating on low speed.
The idea with the two test lights is that they would go in place of the fan motors and would light up during testing. So the light(s) come on = fans would get power and turn on. That would show that the control circuits are operating and that the fans are the problem. I've used headlight bulbs as test lights in those cases because they are a larger load, many don't have them just laying around though. So just a common test light will work.

No rush. Take your time. We will be here.