98 chevy prizm headlights and cooling fan always on car wont run

like all cars with elect fans.
1: stuck relay
2: stuck signal controlling said relay

on older cars the controlling factor is the fan over temp switches
on newer cars the PCM controls all that.
the best way to fix cars is to get the book.
the book is called FSM. factory service manual.

alldata.com

or at toyotanation, dot com.
prizm = corolla.

if the cables were put on wrong yes..since it sounds like you are not mechanically proficient, go to a shop that specializes in auto electrical..they should be able to fix fairly inexpensively(cheaper than the dealer)..

I have run into one with similar issue, open the bottom of the fuse box assembly and look for fried wiring under where the relays mount.

Fix your car right away by clicking the link I attached Chevy Prizm 1998 2002 Factory Service Workshop repair manual download

It can be faulty fan relay.The relay is not turning the system off.Or its wire short issue.Even with ignition off ,the fan relay is getting power so its not letting the fan to turn off.Bypass the fan control relay and see if still the fan works with ignition off or not.

For more troubleshooting check the link below:------

Cooling Fan Stays ON with Ignition Off?

http://whatisbyme.blogspot.in/2012/07/cooling-fan-stays-on-with-ignition-off.html
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Cooling fan relays location ?

http://technoanswers.blogspot.in/2012/02/cooling-fan-relays-location-on-1998.html
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DIC says "COOLING FAN FAULT"?

http://schematicsdiagram.blogspot.com/2011/12/dic-says-cooling-fan-fault.html
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Heater fan and headlights will not turn off with ignition off?

http://technoanswers.blogspot.com/2012/01/heater-fan-and-headlights-will-not-turn.html

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Fuel pump relay and cooling fan relay troubleshooting ?

http://repairhelpcenter.blogspot.com/2011/10/fuel-pump-relay-and-cooling-fan-relay.html

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Where Is Radiator Fan relay and Fuse Located?

http://schematicsdiagram.blogspot.com/2011/12/where-is-radiator-fan-relay-and-fuse.html

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These will help.
Thanks.

I would suspect you have a defective ignition starter switch, this is the main switch the the ignition key cylinder operates and it powers up the while electrical system,. It is under the steering column covers.

Yes, you could wire them to run anytime the ignition is on, but that is not a good idea. Have you checked the fuse? Have you checked to see if the fans actually work? Turn the A/C on and one fan should run continuously. Have you replaced the thermal relay for the cooling fan? You need to just find out why they do not work. Running them continuously is not a good idea. You want the engine to reach full operating temperature as soon as possible. And you do not want to be constantly cooling it down by running the fans all the time. This will cause poor fuel mileage.

I think you have a bad shorted battery or bad alternator.

Compressor could not work without cooling fan comming on.
Check compressor mounting bolts and belt placement on pulley regarding the noise.
But before we get to the a/c system repairs its important to have a properly working cooling system.

Is the car overheating ? It should if neither fan works.
If I recall correctly the fan switch is usually on the upper radiator hose coupling.
you may want to test the fan(s) its self. Remove the electical connectors fron the fan(s) , fabricate a set of jumper wires and run it from the battery. If this works the fan(s) are ok . If it doesn't replace the ones that don't work.
The coolant switch aka fan switch is usually tested with an ohmmeter . Use shop manual for testing procedure.
Test the a/c fan and engine cooling fan relays. (see shop manual for details)
Then I would start looking at coolant( correct mixture and thermostat) although the thermostat is not likely to cause this.
If all of this still doesn't correct the problem it may be the ECU that monitors this system it may not be responding to the signal /voltage from coolant temp sensor to turn on the fan, (again nedd shop manual to test this)
Once you have a properly working cooling systemnow you can turn your focus on the a/c. Compressors either work or they don't.For you safety I recommend having the a/c system serviced by a ASE certified Technician or a tech's who legally can perform a/c service. Good luck

If your car makes bubbling noise and loses fluid then replace coolant cap. It fixed mine and is cheap fix.