The blower motor is probably busted, or the blower speed switch could be busted as well, if that isn't it could be a fuse for the blower motor I would check that first and save your self alot of time and money.
The compressor could be bad.
If you mean an AC - air conditioner compressor, definitely yes. Assuming that the drive belt is not an issue and the cars computer will allow it to senses the disconnection. You could if it was an air conditioner compressor but it would be hot!
Compressor is having trouble starting and is failing on the overtemp protector in the motor. Could be the capacitor or the compressor itself is bad.
Heatstrips could be on with ac
I am also experience same problem with my Toyota Corolla 2008, is it the coil / radiator, fan clutch or compressor. if anyone could address the problem that would be great.
Could be the clutch is gone. If that is the problem, you can have just the clutch changed, but don't wait too long. If it is the bearing, then have to change the compressor. When it is running, you will see the clutch wobble. The clutch can be changed with the compressor on the car. There is room.
It needs to be re gassed
Often this is the connection to the clutch on the compressor.
The most common cause would be low refrigerant.
if the compressor dont come on when you turn on the a/c then your compressor could be bad, also there is a relay in the fuse panel for the a/c compressor is it has gone out then that could cause it if your compressor comes on then you might need to recharge your system
The bolts holding the air conditioner compressor could be loose or the A/C pulley could be out of balance.
thermostat could be bad, or location of it, air flow over it.