Lost power steering. The belt seems fine and

Power steering pumps begin to make a loud whirring noise when you turn the wheel. As long as you have fluid and the power steering is working there is no damage occurring. But either gets worse it is time to change the power steering pump.
As for the belt if it is serpentine style. (Long and makes many turns) then the belt is fine. If it is the V-belt style (old style) only on 2-3 pulleys max then just make sure it feels snug.

Take a look at the reservoir. What color is the fluid?
The fluid may need to be filled or flushed. Everyone allways seems to forget the P/S fluid, Brake fluid, and trani fluid. Oh well, So anyways if the fluid Isn't clean or low that could be the problem. If it is fine but you hear a loud whining noise and/or the fluid is foaming you may have a leak in the suction line or a defective pump.

With the power steering quitting immediately, it indicates a broken belt or serious lack of power steeering fluid. If it's fluid, you have a leak allowing it to escape.

The "tapping noise" sounds like it might be the belt flapping around with engine running.

There is a "pressure regulator" located in the pump just behind the high pressure line that directs high pressure fluid to the steering rack when you turn the steering wheel. It sounds like the regulator valve is sticking and not sending the high pressure fluid to the steering rack when you turn the wheel.
You can remove the pump and clean the valve, reinstall the pump and flush the steering system with fresh fluid or replace the pump and flush the system with new fluid.
Good luck.

It is most likely you just turned the wheel to the farthest limit of its travel, and the power assist cutout at that point.

Check your fluid level to make sure its up to where it should be.

If fluid is fine, I wouldn't worry about it...it is fine and a normal occurance.

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Checking the level of the power steering is a good start. The pump is mechanical, driven by the serpentine belt, and cannot be turned off. Your steering may seem normal but if you let it go, low fluid can destroy the pump.

Dealer, but did you check the Power steering fluid level??or any leaks. There are two hose that connect to the gear box from the power steering pump. if the pump is low on fluid you lose your power steering, if the hose has a leak or it blew and lost the power steering fluid then you lost your power steering again. 
Check the fluid level to the power steering pump and any leaks or broken hose to the gear box.
Keep me posted, be glad to help and good luck.

Is there a large puddle under your vehicle? Your car's power steering is powered by power steering fluid and the belt turning this pump. So either you ran out of fluid due to a slow leak, the belt is not turning the pump, or you have a large leak and you lost all of your fluid at one time. It would be a good start by checking the power steering fluid, and the belt.

Could be two problems. First the power steering; Check the tension of the drive belt for the power steering and the condition of the belt. If that appears to be OK, check the level of the fluid and its condition or apperance compared to new fluid that is recomended by the manufacturer. If that appears OK, it could possibly be the power steering pump it self. Second the clicking; It is most likely a bad CV (constant velocity) axle. Good Luck.

Usually (and I say this without having heard it myself), the noise is caused by a loose or worn out belt in the engine. The best thing is to have it looked at, or if your not worried and you think the belt is fine, buy some belt lubricant at your local automotive