Steering problem
1996 Chevy Tahoe V8 Four Wheel Drive Automatic 301000 miles

for the last year or so, the pwr steering has occasionally hesitated working until you turn the wheel once or twice, especially on a cold AM.
Yesterday, in deep snow, working my way out of a snow bank, it quit completely. I looked at the resevoir and did not see any fluid circulating so I replaced the pump. It didn't help.

How do I properly diagnose the problem, or is this pretty plainly a problem with the power steering box. If so,
is it rebuildable without removeing the whole box, or is that false economy.
Is the box replaceable by a capable weekend mechanic without special pullers for the pitman arm etc.
Lastly, what is the possiblity that I got a faulty reman pump from the parts store?

Thanks, Brian