Steering damper is just another shock absorber that prevents the front wheels going all over the place when hitting a bump. If that fails you feel it badly in the steering wheel. Powered steering you feel the worm gear stiff either left or right and hard to turn but doable. pumps fail from the belt or the drive cause low pressure to the steering gear unit.
You don't mention what vehicle you have for a better answer.
A new (Britpart) steering damper is only £20 (ish) and is a real easy job to do yourself (part# RTC4472).
I'm a Terrafirma fan and thier HD damper is just under £50. their return to center version (which I am a big fan of) is around £70
l fitted the Terrafirma RTC steering damper to my 110 and it's made the steering so much better for road use, the self centering is better and it's more positive to drive on the motorway with much less constant steering correction needed.
Off road it seems pretty much as before l fitted it.