Fan tried to wire directly but fan does not run

You can run without capacitors, but only high speed.

No. If anything it would be the opposite. A bad water pump would cause the engine to run hot and the fan to cut in.
It sounds as though the fan operation is the problem. Assuming it is a normal operating system and not the new fandangled all singing all dancing pain of a system that new electronic management systems can be, then try the following:
1. Check your fan fuse in the fuse box. Replace if necessary
2. Locate the fan and you should find 2 wires, the feed and a ground/earth. Disconnect and run fresh wires (live and ground direct from the battery) direct to the fan and see if it runs. If it does run then the fan is fine. If it doesn't then the fan will need replacing.
3. The fan automatically comes on when the engine reaches activation temperature and is controlled by a temperature sensor in the vehicle. Follow the 2 wires from the fan and you will find they run to the sensor (it usually looks like a bolt or plug with 2 prongs the wires are attached to, somewhere in the engine to detect the temperature). Disconnect the 2 wires and touch them together. With the ignition on the fan should cut in. If it doesn't (and it did when checking the fan directly before) then the sensor is faulty and needs replacing. A new sensor is usually cheap enough just a few dollars/pounds/euros etc.
Hope that helps. By the way, you start off by asking about a bad water pump. If you suspect a bad pump, then I would get that looked at pretty quick as once they start going bad it starts costing a lot to put right the longer you leave it. If it was just a thought because of the fan issue, then if the above resolves it then no worries.
Good luck, Steve.

check manual to make sure it is running in the right direction. if it has been tampered with or took apart before then there are 2 wires leading to the fan,if you reverse these wires it wil run opposite direction

It is amazing how many questions are here for 1999 Dodge Dakota. This is an electric fan I assume. Try running jumper wires from battery directly to fan motor. Does not run= bad fan motor. Runs= thermostat switch likely bad, or bad fuse or wiring.

bad wiring, dirty or melted fan motor, or if the fan motor smells burnt when you smell it try running a positive and negetive wire down from your battery to the wires to the fan and see if it works if you hook them up for a second if it does start working when you hook the wires from the battery up directly to the fan its means the original wires for the fan are either shorting out or losing connection somewhere

An abrupt cycle of power can cause a motor to run backwards. If you turn the power off again and wait 10 seconds or so (enough for blade to stop spinning) it should run the right way. Put the capacitor back the other way and try again.

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It's just a direct wire to the relay. The way the system works is the engine temperature sensor signal the ECM which signal the Relay. The relay is direct to the fans and the fuse. The Relay and is also controlled by the by pass switch from the A/C unit which sends signal to the Relay and from Relay to fans direct to battery and fuse. Hope this helps. If your still not getting the fans to work, check the ground wire and then try running a direct wire from the Battery. If it's works then replace the relay if the fan does not work with the direct wire, replace the fans. Good luck and hope this helps. 

I am having the same problem, sometimes it runs in the wrong direction, blowing the air down. Sometimes something gets tripped and I need to turn the thermostat to off and wait a bit then restart it. If I am lucky it will run int the correct direction and also will warm the house. Sometimes it send nothing but cold air to the house's forced air.

Most fans plug into the wiring harness, plug could be corroded, also look for a ground wire with a rotted connection. Of course the fan could be bad, try wiring it direct to the battery to test it. If it works you may have a bad sensor that simply isn't telling it to come on, good luck,Chuck

There could be a lot of causes for this. If the thermostat is stuck open, the computer will read that as the engine running cool and not turn the fans on. Also make sure to check the coolant temp sender units are working properly. More direct reasons could be corrosion or damage the the wiring of the fans themselves. Try wiring the fans to a direct source of voltage and see if they work. These key steps should put you in the right direction.