Suburban won't turn over

A few weeks ago I started having issues with
starting that I guessed was a dead battery because
it was below zero weather. That starter would click
and kindof act like a low battery. I thought it was
weird because it is a new battery so I guess
alternator. I pulled the battery and alternator out
and took them to auto zone and the battery was
low so that charged it and then it tested ok and the
alternator tested ok. After reinstalling them and
trying to start all of my lights turn on but no
cranking or clicking or anything. Then I thought
starter so I pulled it out and had it tested they
checked it twice and both times it was ok. I
reinstalled it and then when I tried to hook up the
battery it would turn over. So I took the starter out
again and moved the big and little wires (they were
touching I think). I also rotated the starter relay and
rear defroster. It started right up. I drove around the
block then parked it. I tried right after I shut it off to
start it again and nothing, lights but no cranking.
So I rotated the relays again with the headlight
relay. And still nothing but the headlights still
worked. I then rotated and tried every relay in every
different spot and it never changed, lights all come
on including headlights and no cranking. Any ideas
what that could be