Blower fan only runs in positions 1-3, not on 4; relay or resistor?

The blower motor relay is energized when the Blower Motor Control is set to the High position. This removes the blower motor resistors from the circuit and battery voltage is then applied directly from the HVAC BLO fuse (RH IP Accessory Wiring Junction Block) to the blower motor though the relay switch contacts. The blower motor then runs at high speed.

HVAC Blower Controls Circuit Description
The blower motor is a variable speed motor. The motor operates at a higher rate when voltage is increased to the maximum level.
The blower motor resistors reduce the voltage supplied from the A/C FAN fuse (LH IP Accessory Wiring Junction Block) when the blower control is set at low and medium speeds (speeds 1-4). The blower motor relay is energized when the Blower Motor Control is set to the High position. This removes the blower motor resistors from the circuit and battery voltage is then applied directly from the HVAC BLO fuse (RH IP Accessory Wiring Junction Block) to the blower motor though the relay switch contacts. The blower motor then runs at high speed.

Check the AC fan relay
Symptoms Of A Defective Blower Motor Relay
The blower motor relay's job is to basically bypass the current that passes thru' blower motor resistor and deliver it directly to the blower motor. With the blower motor getting full battery current, it'll run in HI speed.

The most common symptom you'll see, when the blower motor relay fails in your Chevy S10 (GMC S15), is that the blower motor will not run in HI speed (but will run in LO, M1, and M2 speeds).

In some cases, the blower motor will fail and the blower motor will not run in HI but you'll have all of the other speeds working.

https://easyautodiagnostics.com/gm/2.8L/blower-motor-relay-multimeter-test-1

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Even with the mode switch in off position? The mode switch is tied into the circuit for the heater speed control switch.

Other than that, I don't know. Are you sure you replaced the right relay, the blower motor relay?

It would help to know the make and model. Different manufacturers put them in different places and mount them different.

Well according to the wiring diagram, the blower relay gets power from two sources and feeds the fan switch. High speed bypasses the resistor and goes directly to the blower motor. The other speeds go thru the resistor and the motor is grounded.
The AC control panel is connected thru the low speed which would include the other speeds also.
The only thing I could think of would be a break in the wiring or one of the connectors.
Did you check for voltage coming out of the switch for each speed, and then coming out of the resistor too ?

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 !!!!.

No.

Probably not. If it runs on high, it is probably good.
Unless is sounds slow or 'tight' on high, or squeaks or chips , etc. Run the fan with the engine off and then shut the fan off and listen and see if you can hear how long it takes to slow down. If it stops in just a second or two, the bearings are tight (dry). If it spins down normally, maybe three to eight seconds or more, the motor is fine. You really don't need this check.

It is most likely your blower relay.
Most cars have one or two relays to control the fan motor, which is a single speed motor that the relays and speed switch and blower resistor control the power to.

One relay is for high speed, also switch contact.
One relay is for other speeds and divert current through a blower resistor located by the fan duct under the dash or under the hiid by the fan.
Also the switch contacts for each speed.

It cad be the dash switch, which has to handle the blower resistor current for all the lower speeds is burned out at those speeds.
It can be the low speed blower relay, as I mention above, is burned out, this is most frequent cause.
it can be the blower resistor is burned out, this can give no low speeds, or loose speeds below a certain speed setting.

Try you manual for the blower relays' positions. Try swapping with the horn relay to test if it is the same type of relay.
Take out the blower resistor carefully (pretend you are defusing a bomb or playing "operation" game as it has exposed coils that are delicate and if you bump the sides of the opening as you extract it you will damage it and short the coils against each other). the wire coils are very fine bare wire coils that look like springs and if touching can burn out.
Switch is harder to test because hard to get at, check the other things first.
You should be able to test for voltages at the resistor plug to see if power is coming from the switch, but wiring schemes can vary.
Post back or use shop manual to troubleshoot the switch.

I would suspect the Blower Resistor. Its there near the blower motor.

under the glove box there is the motor housing with the resistor on the bottom.

I dont know what the car uses , but it could be the resister if equipped , or relay. more than likely a relay on that year