Whining noise i'm hearing a whining noise in my 1993 mercury cougar and the wheel locks up no steering at all what can be done?

it indicates that when the pump gears are placed under pressure /load that they are interfering with the pump housing or are not being held in the correct mesh situation
the situation of powers steering that when in the relaxed position ( no steering wheel movement) the valves are so placed that the oil is by passed straight back to the reservoir but any movement of the wheel closes those valves and diverts the oil to the cylinder/actuator and so power assists the steering
AT this point is when load is applied to the pump and the noise is heard
I would suggest that the pump be removed and inspected for wear on the idler gear shaft, wear on the tips of the teeth from contact with the housing
Mostly the best fix is a replacement pump because it the clearance between the teeth and the housing is excessive or scored then the full pressure will not be achieved

check left front wheel bearing or cv joint

Do a complete P.S. fluid flush. Running the system when low can burn the fluid.

If your talking about a whining noise while driving over 20mph, it's probably a wheel bearing noise, I have written an article and created a video about wheel bearing noises, it will give you a better understanding of what it is and the noises it can make.

Assuming it is not the gearbox (gears can whine). See if you can locate the area. As a starting point check items with bearings - Alternator, water pump, check the fluid for the power steering (this would be my first thing to check),

turn the wheel one way or the other using lots of pressure while trying to gently turn the key

Do you know which belt is making this noise? Usually it's the power steering belt, and sometimes it's the alternator belt. The power steering belt will make noise turning the steering wheel when stationary, the alternator belt will slip as you quickly rev the engine by blipping the throttle. In either case tightening the belt to the specified tension will fix the problem.

check if you got rack in pinion steering the mounting bolts for looseness .check tie rod end housing seats and the inner tie rod ball studs for wear.if all is good.your rack has worn pinion bushing and rack bushing.

I had the same problem with my 2002 Mountaineer at about forty thousand miles. Murcury replaced the steering column free under warranty. I now have ninty two thousand miles and it's back. The rear end is making a whining noise, the tranny is starting to slip, and the rear window regulator went out. Why did we buy a Mercury?????? Disgusted Dave!!!

if its more of a whining its your power steering pump.