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I have a C5 ZO6 track car. It has intermittent but persistent starting problems that act like the ignition has bad contacts or low voltage. The battery and alternator are new. I have been through the frame grounds with a fine tooth comb, disassembled, cleaned and reassembled them.All have good continuity. The battery has been discharging over the course of a week of non use and I found that the ABS, PCM and approach lights all have 12 volt power across the fuse in the engine bay fuse box with key off and out. When starting problems happens the starter solenoid clicks on and off rapidly like low voltage but successive key rotations will often correct what ever is causing this and will start it. I have also just noticed that the fuel range indicator says low with a full tank. In the absence of any other diagnosis by your electrical guys I think I want to replace the ignition switch and the starter solenoid. It seems that some main power switch has intermittent contact problems. I have not been able to remove and check the large relays in the cabin floor fuse box and suspect that one of these could also be the problem. I have a serious time problem and need a solution by Friday.
I would almost bet it is your Ignition Switch! I had almost the Same exact problems you are describing. I check everything you did and then some.. Even had the Car at the StealerShip for a Week and they couldn't figure it out.. This repair is easy and if you need anything I'll do what ever I can to help.. Took me 2.5 Hr Total to do... Cost nothing.. and fixed my car..
If the starter is "clicking" then you have 12v there, just not enough current.. which is usually nothing more than a loose connection or the wire has become too corroded (and that can be INSIDE the sleeving so hard to see). If that isn't happening every time you turn the key, I would look at the ignition switch FIRST, and check the big fat wire going to the started.