Nobody asked you about battery cables. If you replaced those with OEM replacements, then you still have the POS Crappy Azzed OEM Battery Terminal Connectors on the ends and they SUCK! Just those OEM terminal connectors can cause exactly what you are describing. If you have the OEM terminal connectors, replace them ASAP with a quality aftermarket set, like Stingers or whatever brand you want. Should be the first mod done to every H3.

 

#PIP4575B: Intermittent Click No Crank Or Brief Crank No Crank With DTCs - Possible Crank Sensor - keywords BQMI - (Mar 11, 2009)
Subject: Intermittent Click, No Crank or Brief Crank, No Crank with No DTCs - Possible Crank Sensor
Models: 2004-2007 Chevrolet Colorado2004-2007 GMC Canyon2006-2007 Hummer H3with Inline 4 or 5 Cylinder Engine(RPO Codes LK5, LLV, L52, or LLR)This PI was superseded to remove the 4.2L LL8 engine. Please discard PIP4575A.
The following diagnosis might be helpful if the vehicle exhibits the symptom(s) described in this PI.
<a id="d68069e36">Condition/Concern:Some customers may complain about an intermittent no crank, no start but advise that it will start normally if they release the key from the crank position and turn it back to the crank position again. Some customers may also advise that they hear the engine crank for a split second, or hear a click from the starter solenoid, right before the no crank occurs. The engine will always start on the next key cycle as described above so the customer should not have any comments about being stranded if this PI applies.
Upon inspection, no DTCs will be stored. If you verify the concern and take a Tech 2 snapshot of PCM Electrical/Theft Data while holding the key in the crank position, you will see that the Crank Request Signal Parameter reads "Yes" but the Starter Relay Command Parameter reads "Off" during the no crank. If you take a center trigger snapshot that shows the engine cranking for a split second before it stops cranking, you will see that the Crank Request Signal Parameter reads "Yes" but the Starter Relay Command Parameter switches from "On" to "Off" when it stops cranking.
<a id="d68069e49">Recommendation/Instructions:If this exact concern is encountered, check for a power mode mismatch by operating the ignition switch as outlined in the Diagnostic System Check, Power Mode Mismatch, and/or Power Mode Description and Operation Sections of SI.
If a power mode mismatch is found, repair the concern as outlined in SI. If a power mode mismatch is not present during the concern, remove the CKP sensor, clean the CKP sensor bore out with a shop towel, replace the CKP sensor with a new one, and re-evaluate the concern.

 

Thanks Doc olds, the cables were replaced with after market cables several years ago. The dealership checked the crank position sensor and said it was good. I guess I'm going to have to take it back to them!