Solved, I think!
It turns out I had 3 problems at the same time, simple, basic problems but on top of each others:
the battery in the Suburban was actually dead, would not hold the charge: put a new one in;
my battery cables were shot, for some reason, they had been good to me for 15 years but now, they could not carry the current anymore...;
I had to add a new ground cable, between engine block and battery, which is funny since my truck was starting fine before, without this cable...
Now the starter spins fine!
Thanks for your help, it has kept me going and I have learned a few things along the way!
Last edited by wave1957; 09/11/2010 4:27 AM.