High cool and low cool not working

The engine cooling fan system consists of 2 electrical cooling fans and 3 fan relays. The relays are arranged in a series/parallel configuration that allows the powertrain control module (PCM) to operate both fans together at low or high speeds. The cooling fans and fan relays receive battery positive voltage from the underhood fuse block.
During low speed operation, the PCM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. This energizes the low speed fan relay coil, closes the relay contacts, and supplies battery positive voltage from the low fan fuse through the cooling fan motor supply voltage circuit to the left cooling fan. The ground path for the left cooling fan is through the cooling fan s/p relay and the right cooling fan. The result is a series circuit with both fans running at low speed.
During high speed operation the PCM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. After a 3 second delay, the PCM supplies a ground path for the high speed fan relay and the cooling fan s/p relay through the high speed cooling fan relay control circuit. This energizes the cooling fan s/p relay coil, closes the relay contacts, and provides a ground path for the left cooling fan. At the same time the high speed fan relay coil is energized closing the relay contacts and provides battery positive voltage from the high fan fuse on the cooling fan motor supply voltage circuit to the right cooling fan. During high speed fan operation, both engine cooling fans have there own ground path. The result is a parallel circuit with both fans running at high speed.
Your best bet would be to take your vehicle to a qualified repair shop !
Relay Driven Dual Cooling Fan Diagnostics

Replace the fan relays. The Radiator Cooling Fan Motor Relay is located: Under hood, driver side, front side of strut tower, mounted in relay panel
Application:
High speed The Radiator Cooling Fan Motor Relay is located: Under hood, driver side, front side of strut tower, mounted in relay panel
Application:
Low speed,here's a new part.
http://www.autozone.com/cooling-heating-and-climate-control/relay-radiator-cooling-fan-motor/duralast-relay-radiator-cooling-fan-motor/plymouth/voyager-2wd/1996/6-cylinders-3-3-0l-mfi/412240_0_0

there is 2 fuses that you have to check
one will be in the big fuse assembly in the engine bay, the other probably in the fuse assembly in the cab
If they prove ok then it is possible that the coolant temperature SENSOR is faulty and needs replacing
don't confuse it with the temperature sender which operates the temp gauge.

Bad fan motor. Multi-speed motors have a set of windings for each speed. Your high speed is bad so the only solution is to replace the complete motor. When motors are going bad they will over heat and kick out on the heat safety. As it cools back down it will start again for a short time again until it gets hot again.

Hi Maria , The A/C system wouldn't keep the fans from running but none working cooling fans will keep the A/C from working ! This is a fairly complex system if your not familiar with this sort of thing ! I will add the description from the factory service manual.
Cooling Fan Control - Two Fan System
The engine cooling fan system consists of 2 electrical cooling fans and 3 fan relays. The relays are arranged in a series/parallel configuration that allows the powertrain control module (PCM) to operate both fans together at low or high speeds. The cooling fans and fan relays receive battery positive voltage from the underhood fuse block.
During low speed operation, the PCM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. This energizes the low speed fan relay coil, closes the relay contacts, and supplies battery positive voltage from the low fan fuse through the cooling fan motor supply voltage circuit to the left cooling fan. The ground path for the left cooling fan is through the cooling fan s/p relay and the right cooling fan. The result is a series circuit with both fans running at low speed.
During high speed operation the PCM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. After a 3 second delay, the PCM supplies a ground path for the high speed fan relay and the cooling fan s/p relay through the high speed cooling fan relay control circuit. This energizes the cooling fan s/p relay coil, closes the relay contacts, and provides a ground path for the left cooling fan. At the same time the high speed fan relay coil is energized closing the relay contacts and provides battery positive voltage from the high fan fuse on the cooling fan motor supply voltage circuit to the right cooling fan. During high speed fan operation, both engine cooling fans have there own ground path. The result is a parallel circuit with both fans running at high speed.
Do you have a check engine light lit ? The thing to do would have it check at the dealer or a ASE certified repair facility ! They could hook up a advanced scan tool an diagnose fairly quick ! Or you could find a wiring diagram an try testing with a volt meter yourself ! But watch yourself so you don't short out the PCM - engine computer !

It's the mode switch contactors for the high setting just overview the wiring of the high cool or high fan contactors if it's not there check all leads for the high fan or high cool circuitry.

You have a bad board or bad switch. I would say board. You can have service tech check this out. There is only so far you can go without knowledge of Controls ad electricity. Russ

if motor works on heat, but not on cool ,then the low speed is energized by the heat strip or control board .if the motor doesn't run in high on cool, then the fan relay or black high speed tap from the board is not being energized. usually its the fan relay ,which is only a factor in cool in high speed fan mode. try turning fan to on at stat. that energizes fan relay and blower should run in high. gently tap the side of the fan relay and see if fan comes on all of a sudden. if it does the relay is bad. change it wire for wire label all wires and use exact replacement relay unless you know how to read wiring diagram then you can use a 90-340 generic fits all replacement. trace motor power wires back to relay or control board to find where they are fed from.

Compressors on these units runs at only one speed. The change to high cool is only a change in blower speed moving air faster over the cooling coil. I would have the running capacitor for the fan motor checked. A bad capacitor can cause your type of problem. The other problem could be that the high speed winding in the fan motor is bad. Try it operation in the fan only position through the two speeds. If it works in the low and high speed for fan only your problem could be in the selector switch.

You may be right in looking at the motor. It uses a different speed on heat than cool. The heat cycle uses low speed, usually red. Some manufactures use blue (medium). Cool uses black, high speed. If you are confident, switch the low speed wire with the high speed and see if this changes anything. If the fan motor isn't the problem, check the other setting (cool) if the overload trips, you may need to look into a new capacitor or compressor, if so, you can install a hard start kit. these are start boosters, and are inexpensice, sometimes they will give another year out of the comp. but I've put them on and they have lasted 5 years.