My AC is not blowing cool air. Compressor clutch is not getting engaged. AC button is showing green light indicator though. I am suspecting clutch relay problem. where is air conditioning clutch relay in 2004 corolla? I looked in the fuse box under the hood. Couldn't figure out. Appreciate your help.

HVAC FAILURE IT IS CALLED AND COOLING ONLY FAILS.
so what causes this , well in the macro view , it is one of 2 things
the under dash parts are bad.
or under hood parts are bad. (or both ,eeeks)

we do tests to find which side is failing. using tools and hands.
the blower in the dash must blow air, heard and felt
the dash light indicator shows AC is active, if not turn that on.
then the under hood clutch on the compressor engages and the belt to that clutch is not missing or loose, too.

now the compressor spins, if not we diagnose that. (ask)
if that all works so far , we check the 2 lines from compressor
and to the dash fire wall , one must get cold.
if yes we test the heater and damper motor actuators under dash
to make sure they are not stuck. (on heat only)
is this what you want,?. diagnosis methods?

or just have wild guessing.????
or
if you read the service manual it may show, the AC has self test feature, my car does, it will show, say, Heat damper failure if true.
or
get the car serviced in auto repair shop.

Try this link
http://partsblog.olathetoyota.com/1511/common-ac-problems/

1. Check if air blows with the fan setting turned to high.
2. Check that the radiator cooling fan engages when the A/C button is pressed.
3. Locate the compressor.
4. Turn on the A/C.
5. Check if the compressor's clutch has been engaged.
6. If the clutch engages, the fault is elsewhere.
7. If the clutch does not engage, check for power to the clutch.

These steps might help find the problem.

look for air bubbles in the dryer peep glass
if system is out of gas air con compressor clutch wont kick in
clutch is replaceable

Your A/C system may have lost its charge of refrigerant, or the compressor may not be engaging when you turn on the A/C, or the blend air door inside the HVAC unit may be stuck in the HEAT position so no air goes through the A/C evaporator.
Start with the compressor. Does it engage when you turn on the A/C?
If so, the compressor is working and the A/C system probably contains enough refrigerant to make cold air, so the problem is inside the HVAC unit. Replace the motor that controls the blend air door (this is a difficult job and best left to a professional since it involves tearing apart the HVAC unit -- about an 8 to 10 hour job!).
If the compressor does not engage when you turn on the A/C, see if it will run by jumping the compressor clutch wire directly to the battery (use a fused jumper wire). If the compressor works when you jump it, and the A/C blows cold air, the system contains refrigerant and the fault is likely a bad A/C compressor clutch relay or a bad clutch cycling switch or pressure switch .
If the compressor does not engage when you jump it, the problem is a bad compressor clutch.
If the clutch engages but the compressor does not turn (the belt will start to slip and squeal), the compressor is loced up and you need a new compressor.
If the compressor clutch engages and turns the compressor, but the A/C still does not blow cold air, the system is probably low on refrigerant and needs to be recharged. If you Have an A/C gauge set, hook it up and see if the system has any pressure.
If it is out of refrigerant or is low, check for leaks, then have the A/C system vacuum purged to remove air. After the air is out, it can be recharged with the specified amount of refrigerant. It is important to get any air out as this will reduce cooling efficiency and may make the compressor noisy.
My advice to you if you know nothing about A/C service is to find a repair shop that specializes in A/C repairs and let them fix your cooling problem for you. Today's A/C systems with automatic climate control are very complex and reuire special tools and know-how to diagnose and repair.

I would check the following possibilities:
1. Is compressor clutch working? - You need to do this when the ac is blowing hot air only - locate compressor drive pulley on engine - rubber belt wraps around it. Start engine and set to max ac. When the ac is blowing hot air, look at the center of the compressor drive pulley using a good flash light - watch it for a while, it should be spinning with the pulley - this means the compressor is engaged. If not, the compressor is not engaged. If your ac is blowing hot air, then the compressor should be engaged and running (trying to cool). If it is not engaged, then your compressor clutch is probably going out. Could be low voltage to clutch, but more likely the clutch is worn out and only working some of the time. Note: if working normally, the compressor clutch will engage and disengage in cycles- but the air should always be cold. If clutch is bad, compressor would need to be replaced (sold as one unit). This is tricky to diagnose and could take some time - you need to do it when ac is blowing hot air but set to max cooling.

2. Low on refrigerant or refrigerant has moisture in it? If your ac blows cold initially after being off for a while, then heats up, and continues to regularly cycle back and forth between hot and cool air, then the system may be low on refrigerant or the refrigerant may have moisture in it that is freezing and restricting refrigerant flow. An a/c shop can check refrigerant level and even replace refrigerant if moisture is suspected.

Could be other issues, but I would start with these.

Good luck

U may be low in Freon gas.
When Freon is low there's low pressure switch that will prevent A/C compressor clutch from engaging to protect it from failure.
So, first check Freon pressure & any leaks form lines & hoses fittings.
Even if the fan is working, that doesn’t indicate proper compressor OP'S.
Look at the compressor front side you'll see the clutch stationary while the AFT pulley moving.

Then put air-condition compressor switch to ON (Engage),
You should see the clutch engage & start rotate,
If NOT, this is very clear indication u r low in Freon.

Regards;
MAR

SEE WHAT COLOR THE AC MAG CLUTCH RELAY IS / UNDER THE HOOD RELAY BLOCK IF IT IS WHITE TRY REPLACING IT WITH ONE OF THE BLUE ONES IN THIS SAME BLOCK (HORN RELAY) IF COMPRESSOR ENGAGES REPLACE WITH TOYOTA UPDATED RELAY ( PLEASE RANK THIS)

if you by passed the relay and clutch engaged then this shows that pump works ??but was it getting cold on and around the restrictor valve where the pipes enter the cab is normally a valve block but american monsters use a valve in the pipe for cooling and if its not getting cold their or blowing cold inside cab then system needs re-gassing with R 134 gas if its an older system with R 12 gas then it will need to have adaptors fitted to valve connections and refilled with R134 gas.The main cause of A/C system loosing gas is porosity in the rubber flexible pipes also the back seal on the pump.Or just regass and put a leak stopper in the system

it could be the air conditioning clutch going out. to check turn your car on and idle it with ac on and hood open. at the ac compressor it will have a pulley on it with a clutch that engages when the air conditioning is on. if it engages and disengages it can be the clutch itself has gone bad, the ac clutch will also disengage if there is not enough freon in the ac system, will also engage and disengage if the pressure gets too high in the ac system. Depending on the year of the vehicle it will disengage at full throttle and come back on when you are not at full throttle.
If it is a metallic sounding screech for example take a coke can and drag it across pavement kind of sound it could be a bad compressor or a bad ac clutch. If it is a more rubbery sound for example a car spinning its tires kind of noise it could be a loose belt.

1. Check to make sure all belts are tight under hood
2. start car and look at ac compressor to make sure compressor pulley is turning and that the fan clutch is engaged spinning