Hyundai Repair: loud squeeling noise with 03 Elantra GLS, power steering fluid, power steering pump

Question
In the past few months my Elantra started making a loud squealing noise. At first it was just when making tight turns, but as time has passed it has steadily gotten worse. I replaced the belts (one snapped, others were dry-rotted, choose to replace all of them) but that didn't work. Upon opening the hood and watching while someone turned the wheel all the way to the left or right the power steering pulley would slow down, catch, or skip. So I replaced the power steering pump with a rebuilt one. However, that did not fix the problem (pump pulley still slows down, catches, or skips). In fact, the squealing noise is so bad (and Very loud) now that it will not go away until my car shifts gears (Only to come back when I slow down and make a turn). All belts are tight, I had to replace the power steering fluid when I replaced the pump, and there doesn't appear to be any air in the fluid.

Answer
The fact that the pump slows down but the engine does not indicates that either the power steering or the alternator/water pump belt is slipping.  It'd be my recommendation to go back and check the alternator/water pump belt, as this belt must be *very* tight for it to not slip.  The power steering belt, on the other hand, mostly just needs to be snug.