Hi
Check the main power connection on the starter.I had a Sunfire that someone had crossed the nut on the starter positive post.That stressed it enough that it was loose in the solinoid,after time the post loosened and the cable end wasn't tight and began to arc.the conection was bad and had the same thing,sometimes would just click we would wiggle the power wire and it would work,some wierd electrical things would happen.Sometimes a boost would do it.
Anyhow a new solinoid and cleaned up the wire end,problem solved,the nut was striped and couldnt be tightened,or loosened.
Thomas
90 Chev 3500 c/c 4x4,6.2na,400 auto,4:10 gears.DSG Timing gears,main girdle, isspro tach, pyro,boost,oil and trany temp.Dual Tstats, High volume peninsular pump,on shelf, Custom turbo and intercooler 85%complete. Change of plans for the dually, it's going to get a Cummins. Both trucks are Blue 90 4x4 crews