Been dealing with this issue for months.
2004 Chevy Suburban Z71 5.3
Sat for a few months because it wasn't running right. Finally got it running good due to clogged cats. Replaced those. Only throwing 2 codes for two bad O2 sensors.
New problem: (Randomly) Does not start or crank. Everything comes on like normal. Starter and relay clicks. Fuel pump engages. No lights on dash except engine light. It won't jump off from batter BUT will jump off from fuse box sunder hood with a wire in the crank fuse slot. Dealing with this problem, we've taken it to the same mechanic about 6 times now and have replaced:
Checked battery- good
Battery cables at posts- good
New ignition tumbler
New ignition switch- underneath column
New starter
New starter relay
New fuel pump
New crank fuse
Please help!!!!!!!!!!!!!!!!!!!!

 

Still sounds like a cable issue between the battery and starter

 

If you haven't found a solution yet, you may want to check the under hood fuse box on the under side for a corroded hot lead at the connector that hooks up to your crank/start relay. Conditions under your hood vary. But, no matter where you live, your cooling system does give off some moisture combined with engine heat and other particles in the air. Such conditions can create an environment which over time can make for some very poor connections at the fuse box where the wires lead into the connector. But, I hope you have already found and resolved your no crank issue.