Steering wheel vibration on 2004 toyota corolla

Siunds like a stuck caliber or a bad proportioning valve.

run fault codes and look for injector misfiring or plug coil problems

There re few possibilities that can cause no idle issues.To troubleshoot the issue help links are provided below.Click the link below:---
Idle Problem? http://whatisbyme.blogspot.in/2012/05/2001toyota-corolla-idle-problem.html
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Idles rough and quits when gas pedal is pressed less? http://technoanswers.blogspot.in/2012/01/1999-ford-f-150-idles-rough-and-quits.html-----------
Stumbling and stalling at idle after engine rebuild? http://schematicsdiagram.blogspot.in/2012/03/stumbling-and-stalling-at-idle-after.html

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Cooling fan Shuts OFF and Idle Drops? http://howtobyme.blogspot.in/2012/05/toyota-celica-cooling-fan-shuts-off-and.html

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Rough Idle and Vibration? http://whatisbyme.blogspot.in/2012/05/2006-ford-f150-rough-idle-and-vibration.html

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Steering Wheel Vibrates at Idle? http://whatisbyme.blogspot.in/2012/05/1993-toyota-corolla-steering-wheel.html

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Runs Fine But Idle Is Low? http://whatisbyme.blogspot.in/2012/05/2004-toyota-highlander-runs-fine-but.html

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Vehicle Will not hold Idle? http://whatisbyme.blogspot.in/2012/05/2003-lexus-es300-vehicle-will-not-hold.html

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Engine Idles Rough and Dies? http://whatisbyme.blogspot.in/2012/05/1994-lexus-es300-engine-idles-rough-and.html

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This will help.
Thanks.

Get the Idle air control valve checked inspected.Also its suggested to get more troubleshooting done.For more troubleshooting,click the help,links below:---Idle Problem? http://whatisbyme.blogspot.in/2012/05/2001toyota-corolla-idle-problem.html
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Runs Fine But Idle Is Low? http://whatisbyme.blogspot.in/2012/05/2004-toyota-highlander-runs-fine-but.html
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Vehicle Will not hold Idle? http://whatisbyme.blogspot.in/2012/05/2003-lexus-es300-vehicle-will-not-hold.html
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Erratic Idle and Intermittent engine stalling? http://technoanswers.blogspot.in/2012/04/1997-toyota-camry-erratic-idle-and.html
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Stumbling and stalling at idle after engine rebuild? http://schematicsdiagram.blogspot.in/2012/03/stumbling-and-stalling-at-idle-after.html
---------Cooling fan Shuts OFF and Idle Drops? http://howtobyme.blogspot.in/2012/05/toyota-celica-cooling-fan-shuts-off-and.html
-------Rough Idle and Vibration? http://whatisbyme.blogspot.in/2012/05/2006-ford-f150-rough-idle-and-vibration.html
--------Steering Wheel Vibrates at Idle? http://whatisbyme.blogspot.in/2012/05/1993-toyota-corolla-steering-wheel.html
--------This will help.Thanks.

The specs are what the manufacturer recommends for the vehicle when it leaves the factory. However that means with the original tires and condition. The caster is not adjustable on a Corolla, so if the vehicle pulls even with the tires switched, there is a possibility there is damage to the strut or steering parts. However, before changing anything, check all tire pressures and make sure the brakes are in good condition. A brake that is not releasing properly will cause a pull to that side. Individual toe is rather meaningless - the total toe is what is measured. You have no king pins on a Toyota so you will not have KPI.

Vibration or a "shimmey" is an indication that the tires need to be balanced. This is not related to the wheel alignment you had done A poorly balanced tire will vibrate on its own, transferring the vibration all the way through the steering wheel. Have the tires balanced. If this doesn't fixy your issue, then the problem lies between the rotors (could have a warped rotor) and the rack and pinion. Best of luck on your problem.
Greg

Could be a tie rod, CV joint, wheel bearing, or even a bushing. You won't know untill you get into it.

It is not the firewall. This means your power-steering engine has gone bad and it might have affected the steering rack.

You need an expert to fix this for you.

Rate this solution please.

Try checking the engine/transmission mounts, one of them may not have been reinstalled properly, or worn out, causing a vibration. If the car is able to move with the new clutch, and it seems to work, I wouldn't say the clutch was put in wrong. Also check the wires around the engine/transmission, you may have knocked something loose as well.
Hope this helps

power steering fluid level, if ok, it sounds like your power steering pump is weak and needs replacing. All the best

Happy to help
HAve a nice day!
tc