Replace the blower motor

Check your switches and blower motor. In a car that old, the switch or the motor could be defective. Did the fan make any weird growling noises before it stopped working?

When you say blower motor you mean the motor that blows heat into the cabin inside the vehicle not the cooling fans for the radiator. I ask because mention relays /more then 1
I find that with blower motors its usellyI not the motor or resistor .The motor will spin with no bearings left in it will make a lot of noise but spin .The resistor olny on most vehicles comes into play on high speed setting olny .
The most common problem is bad connections to the motor it self 9 out of 10 times .Turn the key to run don't start but the fan control on high start wiggleing the connector and the wires around if the motor starts to spin this is the problem .
If not that 1 out of 10 times is likely related to the INT control switch eighter the switch is not being feed power or the switch is shorted inside .
Do you have a test light HOT to GROUND or a muility meter if so you can test for voltage to the connector that plugs into the control switch .No voltage then the problem is fearther back in the system .
Problems like this need some though before things are replaced . You need a starting point a basic understanding of how the circuit works . You start replaceing things to early you end up lost .
Try the wiggleing connector thing its likely your problem.

If your blower motor has only one terminal going to it that means the switch is where the problem is. Blower motors like this are controlled by a switch that has a rheostat or resistors built in to the switch.

When you turn the switch to the low position the fan runs slow because of more resistance thus reducing the voltage to the motor. When you turn the fan to the high position the fan runs at full speed because it is getting 12 volts.

Now some switches use a electronic board to control the speed. You need to do a search and replace the fan control switch.

One other thing - my Volvo had the same problem and I ended up replacing the whole dash module - new it costs $325.00 but I picked one up at the junk yard "pull-a-part" for $35.00.

you will need to replace the blower motor as it has probably siezed going by the squealing noise you say you heard.i`m assuming this has more than 3 speeds for the fan motor.if it wasn`t working on one speed then you probably have a bad blower motor resistor that will need to be replaced as well so you will have all fan speeds.this is located in the air duct housing near the blower motor and will have about 6 wires on it.some of these on under the hood on the firewall anywhere from the passenger side to the center of the firewall.not sure about the vent switch.if the vent switch is moving the doors and you hear a clicking then you may have a vent door problem that the door pivot is worn.

First check the fuse,if ok. Check if you still get power to the blower motor, on the plug, if so. you need to replace the blower motor and resistor. if not check power supply to blower switch,and power after the switch, if you turn switch on and off.

The resistor bank is bad for slow speeds, the switch is bad for high speed. In your test, you have voltage, but the switch wont carry the amps, to run high speed. Open circuits will not blow fuses. Replace both switch and resistor bank for all speeds. Make sure to clean leaves and trash from fan housing and see if fan spins freely.

Don't know where you got your info . The heater blower motor electrical B+ power comes from Fuse F 64 a 40 amp fuse . This goes right to the blower motor on the green with orange stripe wire , The black with red stripe wire goes to the switch for high speed . There is Splice 24 that ties into the black with red stripe wire. The splice 24 turns into a black with orange stripe wire . An this wire goes to the blower motor resistor . All the switch does is route the B+ voltage through the different resistors to ground .

Thermal resistor "usually" stops working is because of faulty fan speed switch ???? Totally not true , resistor assemblies fail because of the heat associated with dropping voltage across the resistors , That is why they put the resistor assembly in the air box . Air blows over to cool the resistors . The switch is nothing more then a way to direct different speeds to ground .

Rather then listening to other people ,why not learn the right way to test electrical circuits .
Electric Testing Techniques You Need to Know

Do you know what a wiring diagram is ?
http://www.bbbind.com/free_tsb.html Enter vehicle info . Under system click on HVAC , under subsystem click on heater . Click the search button , then on the link . Use a volt meter an test , don't guess !

You need to replace the blower motor

Several possible causes (blown fuse, malfunction in blower speed switch, open ground in blower motor electical circuit, burned out blower motor (brushes), open circuit in blower resistor, etc. Best solution, Take the vehicle into a Hyundai Service Center (dealership), pay the diagnostic fee. They will tell you EXACTLY what the problem is and what's needed to fix it (parts, labor, tax, time-frame, etc.)

I had a truck about the same year with the same problem, it was the wiring harness, but id check the resistor and the fan first before replacing anythings,