Load test the battery to make sure that you're getting the proper CCAs out of the new one. Just last month I had battery on my truck that was showing full charge and acted fine 90% of the time, but would occasionally drag when trying to cold start. Wouldnt fire off, then after the third or fourth try, it would spin up perfectly fine and fire right off. I ran up to autozone and threw it on their tester which will load it and the 850 CCA battery, showing fully charged, was only actually putting out 510 CCAs which was/is barely enough to turn it over. I'm guessing there was probably a little burr on the starter armature and if it was in a certain position and hung up slightly, the fully charged but weak battery wasnt producing the CCAs to spin through it. As others said, check the grounds first and make sure all are tight and clean, and I also think on those 97 z71's there was also a starter specific solenoid. Could be that it is going bad. Intermittent electrical issues are the most frustrating problems to chase in the automotive world.