"exact same processor" if its the same processor one works the other doesnt, its not a chipset problem, his processor either got shocked while putting it together or was DOA to start with.
"So I swap processors between the machines and my machine is able to POST just fine with her processor but her machine does not POST with my processor."
You misread the post, the processor in question worked fine in his machine, both processors failed on the machine with issues. Ergo, the processor is not the problem here, either the motherboard is, or some unrelated issue is.