Hello I will help you with your question,
There are two fuses for the blower relay, F2.28 and F2.08 so both have to be good to operate the blower.
If you have a 12 volt testligh you can make short work of this diagnosis.
With the blower motor plugged in backprobe the blower connector at the orange/black wire with the key in the run position and the blower selected on high speed. If you have power there the blower motor, fuses and blower relay are good. The suspect parts would be the resistor or switch if you have power to the orange/black wire. If no power check the pink/white wire and if there is power there the blower motor has failed.
Let me know what you find and we can work from there
By backprobing you insert the tip of the testlight from the harness side of the connector so the blower motor is connected to the wiring harness. In the first test you are measuring voltage through the windings of the blower motor that ensures the motor is not burned open.
Did you check the fuses?
The relay may be the problem as you suspected so we need to move to the relay/fuse block.
F2.28 is shown below along with the blower relay,
Turn the blower on and off (or have a helper do it) and put your finger on the relay to feel if it clicks as the blower is selected. If it does not check the fuse (F2.28)
The relay will work independently of the blower motor so you need to concentrate on the power to the relay coil (F2.28) and the ground provided by the blower switch to the relay.
Pull the relay and use your testlight with the key on, you should have power to two of the sockets for the relay pins. When you find those put one lead of the testlight in a powered socket and use the other to find the socket from the remaining two that switches the light on and off with the function switch
If both of those (power and ground) work then swap the relay with the acessory relay and see if the blower comes on.
You had the function switched to heat or cool? That is what turns the relay on.
If there is not a ground to the relay then the switch has failed and the controls need to be replaced. You said the AC will come on just not blow so the ground to the switch has to be good.
To remove the control head click here
Once you pull the control head check from the yellow to the black with the relay plugged in and the key on (control head plugged in also. You shoud be able to turn the testlight on and off with the function switch. If you only have the light stay on the function switch has failed.
Try the relay in its socket and swap them if needed. You should feel the relay click then power should be at the blower motor. Go back and check at the orange/black wire.
If you have power to the pink/white but not the orange/black with the blower plugged in then the blower motor has failed.
Likely what happened is that the blower was pulling excess current and burned the resistor open so it would only operate on high then running on high burned the blower open also.
Click here for the blower replacement procedure
You can make a final check, have the blower switch in the high position then use the testlight to check from the pink/white to the orange black and turn it on and off with the function switch. If you can do that the blower is the failed part.
You need to replace the blower then.
Please let me know if there is anything else I can do for you