Power steering pump in noisy when first started when cold, 2004 santa fe 3.5, has 62000 miles

sound like you have lost presure switch that is supposed to relive presure when presure is high or the belt is too tight putting presure on the bearing causing over heat or oil cooler restricted and not coolling the oil

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Is it a "wine" noise that gets louder when you rev it up? Sounds like an idler pulley. Is it a 3.3L motor?

Not with a diagram. Clean all the hoses and the pump so that everything is easy to see. Start the engine and get someone to put a little pressure on he steering. You should be able to find the leek.

I have heard of this many times before and sometimes it has been different issues that would cause that.1. look at power steering fluid and see if its very dark in color and if so have system tested for leaks and flushed. If not dirty or no leaks are found you are probably seeing the first signs of a bad power steering pump. Hope this is helpful.

the crank pulleys (also called a harmonic dampener) on these vehicle are a fairly common failure. as they begin to break apart, the pulley will begin to have a wobble as the engine runs, causing the drive belts that power your alternator, power steering, etc to loosen off. when the belts then get wet, combined with being loose, they will slip, causing your accessories not to work. hope this was helpful!

have you checked under the hood ? to check if the drivebelt/s for power steering pump is there and if your engine is diesel the power servo pump may be same belt ? hence loss of both these functions? as you say going thro puddles?? deep ? could have caused belt to come off it will be obvious to see if belt is not there ? hope this helps

HI check your power steering oil pump reservoir filter screen this seats at the bottom of reservoir is probably plug .it can cause the pump to aerate if thats your case replace reservoir.for proper inspection of reservoir completely empty it and check. hope this helps.

Does the Check Engine light come ON when this happens? Whenever the "Check Engine" light comes on, there is always a DTC (Diagnostic Trouble Code) stored in the ECM (Engine Control Module). You'll need an OBDII (On-Board-Diagnostics) scanner to retrieve any codes recorded/set in ECM. Once you do this and let us know what, if any codes are set, then we can go from there.