Good battery but wont crank or take jump, lights dim

1993 Oldsmobile Cutlass Supreme SL, 117,000 mi, V6 3.1, Florida

Won't start and couldn't jump. Clicked, cranked slow but not over. Inside lights dim and/or flickering. Removed battery(Diehard) for testing. Walmart said it's fine. Figured can't be, over to Sears. It tested good there too. Nothing it needed.

Cleaned terminals and reconnected. Still the same. Will check battery cables. My guess is the starter?

Recently car has been leaking or burning transmission fluid, not sure yet. Was getting significant white puff at start up after recent quickie oil change. They overfilled and I had to drain anyway and refill. Also noticed recent hesitant start ups when hot.