Need to see a picture of rack-in-pinion for 1997 buick century

If you mean the accordion dust seal boot the answer is no.

If it won't stay full, then it has to be leaking out somewhere.

check carefully the rack and pinion-where the fluid goes to accommodate power steering-drips or leaks there indicate seals in the rack have gone out. The rack is located underneath, and in back of the engine.

remove the left and right tie rod ends from the from the pivot arms , remove power steering oil lines, remove steering wheel shaft to rack pinion clamp, with wheels in straight ahead position remove rack hold down fittings, slide pinion off steering shaft and remove rack.

Normally a sign of a failed rack and pinion unit.

There are few help links showing exact accurate procedure to replace Rack and Pinion. Click the link below and follow the procedure:-----
Pinion Seal Replace on Dodge Dakota? http://howtobyme.blogspot.in/2012/04/pinion-seal-replace-on-dodge-dakota.html

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How to Replace a Rear Pinion Seal.
http://schematicsdiagram.blogspot.com/2011/07/how-to-replace-rear-pinion-seal.html
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How to replace Power steering rack and pinion gear on Chevy Silverado 2500 HD? http://technoanswers.blogspot.in/2012/02/how-to-replace-power-steering-rack-and.html

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How to replace Power Rack and Pinion Steering Gear on Acura Car Models? http://repairhelpcenter.blogspot.com/2011/11/how-to-replace-power-rack-and-pinion.html

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How to replace power rack and pinion steering gear on Toyota cruiser? http://repairhelpcenter.blogspot.in/2012/02/how-to-replace-power-rack-and-pinion.html

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How to replace Power Rack and Pinion Steering Gear on Acura Car Models? http://repairhelpcenter.blogspot.com/2011/11/how-to-replace-power-rack-and-pinion.html


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Front Drive Pinion Seal Removal on Ford Explorer? http://repairhelpcenter.blogspot.in/2012/03/front-drive-pinion-seal-removal-on-ford.html

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How to Replace Driveshaft, Pinion Flange & Seal?

http://repairhelpcenter.blogspot.in/2012/03/how-to-replace-driveshaft-pinion-flange.html

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How to Replace Power Rack & Pinion Steering Gear On 2007 Ford Taurus? http://repairhelpcenter.blogspot.in/2012/03/how-to-replace-power-rack-pinion.html


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How to Remove Power Rack & Pinion Steering Gear on Ford Windstar? http://repairhelpcenter.blogspot.in/2012/03/how-to-remove-power-rack-pinion.html

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Power Rack & Pinion Steering Gear replacing details for Buick Park Avenue and Pontiac Bonneville

http://repairhelpcenter.blogspot.in/2012/03/power-rack-pinion-steering-gear.html

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How to Replace Power Rack & Pinion Steering Gear on Mercedes Benz Truck? http://howtobyme.blogspot.in/2012/03/how-to-replace-power-rack-pinion.html


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How to replace Power Rack & Pinion Steering Gear on Toyota 4Runner? http://howtobyme.blogspot.in/2012/03/how-to-replace-power-rack-pinion_27.html

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Power Rack & Pinion Steering Gear Replacing on Toyota Land Cruiser & Sequoia? http://schematicsdiagram.blogspot.in/2012/03/power-rack-pinion-steering-gear.html

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Power Rack & Pinion Steering Gear Removal on Toyota RAV4? http://repairhelpcenter.blogspot.in/2012/03/power-rack-pinion-steering-gear-removal.html

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How to Replace Power Rack & Pinion Steering Gear on Toyota Sienna? http://technoanswers.blogspot.in/2012/03/how-to-replace-power-rack-pinion.html

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These details will help.
Thanks.

Your PS pump is fine.

This vehicle has:

Variable-assist power steering: A power steering system that uses valves and speed sensors to vary the amount of steering assist according to engine or road speed. At slow speeds more steering assist is delivered and steering the wheels is easier; necessary for parking, etc.. At higher speeds, steering assist is reduced and more steering effort is required to steer the car, giving the driver greater feel of the road. Also known as Speed-sensitive power steering.

Loss of current to the magnetic coils would cause a loss of power assist at low speed. Coil resistance can be checked with an ohmmeter, and should read about two ohms. An infinite (open) reading indicates a bad coil (requires replacing the rack since the coils are not serviceable). Checking for shorts between both sides of the coil assembly and rack housing is also recommended.

Best wishes

Look to try know where the leak is coming from,the hose,the rack and pinion,or the pump.

The shift solinoids are mounted to the valve body which is behind the side cover of the transmission. Usually you have to lower the trans to remove the side cover, which envolves lowering the subframe. If you drop the subframe the steering rack must be disconnected and the engine must be held from above because most of the motor/trans mounts are on the subframe

you may need a rack and pinion "steering gear". You might try putting some hy-tach oil additive in it first

That would be for an entire rebuilt steering rack assembly, and that is high on the price, no one rebuilds these steering racks, to many problems. I show the Rack cost about $250.00, then 3 hours of labor, labor here is $120.00 pere hour, so the cost with fluids and parts should run about $600.00 + or - a $100.00 or so. Is this new part gold plated?