I have a 2002 Elantra. Yestreday the lower fan speeds on the air conditioner fan stopped working (positions 1,2,3). The High speed (position 4) works. Any ideas how to correct?

Blower motor resistor bad ! Watch this video , Blower Motor Problems Auto Repair Help

If you mean the blower only works on high, it could be the resistor that cuts down the power for the other speeds.

Check and replace fan switch control module located in glove box...$30. part. Do it yourself.

it is the blower motor resistor. I do not know off of the top of my head if it is part of the climate control unit or external for your particular vehicle. However the symptoms match.

The heater blower is normally controlled by voltage sent to the blower via a resistor network.
In this case it seems that this unit also called the fan resistor is defective.
I assume that 4 is the position where the blower is running HIGH and in this position the blower is powered directly without using resistor for lowering the speed of the blower. In step 1 - 3 the blower is powered via the mentioned resistor network.

In my opinion the resistor network is defective.
Replace it !!!!.

If you can access the switch contacts Clean them . They become coroded or out of contact with moisture condensation and gunk sometimes

see if you can get access through dashboard

Yes I would go with the switch, BUT, does it have a resistor bank? That is, how does it reduce the speed? Many systems use resistors to lower the speed. Burnt or bad connections can cause this as well.
You can test the blower motor by connecting direct power from a source like the cigarette lighter if you are handy.
Most of the time the lower speeds konk out but the high speed continues to work this is the resistor bank that goes out.

All cars are designed with a blower fan motor that pushes air through the ventilation system. This air is processed by a series of vents to direct the air to various positions. Example: heater, air conditioner and defrost modes. Most blower motors are power by a basic electrical circuit that utilizes a multi resistor or a solid-state resistor to control different fan speed modes (low, medium low, medium and high). If the resistor malfunctions it may lose one or more of the lower fan speed settings.
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Sounds like a bad blower resistor

From the service manual:

Idle Speed/Ignition Timing/Idle Mixture Ratio Adjustment
NGEC0549
PREPARATION
NGEC0549S01
1) Make sure that the following parts are in good order.
I Battery
I Ignition system
I Engine oil and coolant levels
I Fuses
I ECM harness connector
I Vacuum hoses
I Air intake system
(Oil filler cap, oil level gauge, etc.)
I Fuel pressure
I Engine compression
I EGR valve operation (If so equipped)
I Throttle valve
I Evaporative emission system
2) On air conditioner equipped models, checks should be carried out while the air conditioner is OFF.
3) On automatic transmission equipped models, when checking idle rpm, ignition timing and mixture ratio,
checks should be carried out while shift lever is in “N” position.
4) When measuring “CO” percentage, insert probe more than 40 cm (15.7 in) into tail pipe.
5) Turn off headlamps, heater blower, rear defogger.
6) Keep front wheels pointed straight ahead.
7) Make the check after the cooling fan has stopped.

SEF976U
3. Open engine hood and run engine at about 2,000 rpm for about 2 minutes under no-load.
SEF977U
4. Perform diagnostic test mode II (Self-diagnostic results). Refer to EC-644.
SEF217U
OK or NG
OK ' GO TO 2.
NG ' 1. Repair or replace components as necessary.
2. GO TO 2.
BASIC SERVICE PROCEDURE VG33E
Idle Speed/Ignition Timing/Idle Mixture Ratio Adjustment (Cont’d)
EC-616
2 CHECK IGNITION TIMING
1. Run engine at about 2,000 rpm for about 2 minutes under no-load.
2. Rev engine (2,000 to 3,000 rpm) two or three times under no-load, then run engine at idle speed.
SEF978U
3. Turn off engine and disconnect throttle position sensor harness connector.
SEF975R
4. Start and rev engine (2,000 - 3,000 rpm) two or three times under no-load, then run at idle speed.
5. Check ignition timing with a timing light.
SEF371S
15°±2° BTDC (in “P” or “N” position)
OK or NG
OK ' GO TO 4.
NG ' GO TO 3.
GI
MA
EM
LC
FE
CL
MT
AT
TF
PD
AX
SU
BR
ST
RS
BT
HA
SC
EL
IDX
BASIC SERVICE PROCEDURE VG33E
Idle Speed/Ignition Timing/Idle Mixture Ratio Adjustment (Cont’d)
EC-617
3 ADJUST IGNITION TIMING
1. Adjust ignition timing by turning distributor after loosening securing bolts.
2. Turn off engine and connect throttle position sensor harness connector to throttle position sensor.
SEF972R
' GO TO 2.
4 CHECK BASE IDLE SPEED
With CONSULT-II
1. Read idle speed in “DATA MONITOR” mode with CONSULT-II.
PEF356V
700±50 rpm (in “P” or “N” position)
Without CONSULT-II
1. Check idle speed.
700±50 rpm (in “P” or “N” position)
OK or NG
OK ' GO TO 6.
NG ' GO TO 5.