Also don't forget about the temp sensor.

I had the opposite problem, my fan wasn't coming on after a hard drive, and pulling up to the house and stopping. Sometimes it would go on, then off, then on, of, and click back and fourth. Thought it was the relay located in the fuse box under the hood, swapped it for the power window relay. Windows still worked, and the fans kept sputtering on and off.

Then learned the fans are controlled by the cooling system, aka, where the coolant runs through your engine block. There are two connectors to temp sensors on the engine block. One is located next to the thermostat on the back of the engine, near the distributor, the other is located in the front of the engine, where the upper radiator hose enters the engine.

Here's how to check, get a paper clip, and bend into a "V" shape, so you can stick one end into the green plug. Wiggle it around if you don't make contact. You are basically by-passing the temp sensor (a basic switch if you will which tells the car to turn on the fans or keep them off). Think of it this way, if the temp sensor feels the car is hot, it tells the car to turn the fans on. Now in your situation, maybe its stuck open?

I dunno, try the paper clip method on both plus, one of the back of the engine, and one on the front.

Gotta go to class, will check back in about 4-5 hours. Sorry if not all the info is here, PM me for more info. I have my old temp sensor at home, and can take pics of the areas where they are located.