The first indicator that the system knows there is a problem is the fact that the front pusher fan is running. That fan hardly ever runs, but will run if there is a problem with the puller fan. First off, this is for a '94? right? Other than what has already been stated, there are several things to check:
1) Does the puller fan run at all when you turn on the AC? If not, is there voltage at the wiring pigtail at the fan motor? Disconnect the plug from the motor and test to see if there is voltage with a volt meter.
2) If there is voltage at the volt meter, then that is just about a dead give away that the problem is with the fan motor. Will the fan motor turn at all? (try turning the fan blades with your hand. Sometimes the motor will lock up tight.) If it is locked up, then you definitely need to buy a new motor. NOTE that if you buy a new motor (for the '94 - '95), you will need the 2 speed puller radiator fan, not the single speed pusher fan. The motor is kinda hard to find. NAPA can get it, but the cheapest and quickest place that I found was Autozone. You have to special order it, but they're pretty quick at getting it shipped. You might want to also remove the fan shroud from the car and plug 12 volts directly up to the fan to see if it works.
3) The second thing to check is the 60 amp fuse in the power distribution box under the hood. The fan pulls alot of current, and tends to cause the fuse to get really hot and sometimes melt the wiring and start charring one side of the fuse. The 60 amp fuse is the yellow ones. Check your owners manual for the specific one for the fan.
4) The third thing to check (if you don't have power to the wiring pigtail) is the PCM relay module (sometimes called the IRCM) which is a small metal black box that is mounted just in front of the air filter box. This box contains multiple relays that control different things...with the fan motor being one of them.
5) The last thing to check is the coolant temperature sensor that is mounted on the pipe on the right side of the intake manifold. There are two coolant temp. sensors. The one mentioned above sends its info to the computer and the temp is used for engine management. The other temp. sensor is mounted next to the thermostat and is only for the gauge on the instrument panel. Anyway, you can check the resistance across the sensor with an ohm meter (or multimeter), to see if it's reading correctly. If you unplug this temp sensor with the car running, the computer should turn on the radiator fan motor on high speed because the signal from the sensor has been lost.
Of all of this, I would definitely suspect the motor first. I've replaced 2 of these motors for my '95. The last time was just last week. In my case, the motor would run for about 5 minutes, and then shutdown. You could shutdown the engine and let sit for 10 - 15 minutes, and then the motor would run again for 5 minute and shutdown again. I checked all of the other stuff, and then figured out that I still had 12 volts at the wiring pigtail even when the motor stopped at the 5 minute mark. I replaced the motor and everything is fine. There must be some type of thermal switch in the motor that was shutting it down because it was overheating for some reason. Check the 60 amp fuse in the power distribution box (under the hood) also. I ended up replacing the fuse in mine. The fuse wasn't blown, but one leg of the fuse had gotten really hot at some point in time that it had turned brown. If you do a search, you will see lots of people saying they have problems with the IRCM. I have not had any problems with mine, and it is now 12 years old. Others say they had problems with the coolant temp sensor, but you can check that one quickly to see if it's reading correctly. I found a table of resistance conversions for the sensor on Auto Zone's website for that sensor. Mine was reading fine. If you do need to replace it, it's really cheap.... ~$10.00 - $15.00
Good luck.
David