Conklin, what you report I also experienced when upgrading all (3) of my BP6 systems to single CPU: P-III/1100E@1.21GHz.
For each system, after the new CPU/Neo370/HSF was installed, it would not boot. For each system, when I switched to the alternate socket, it booted right up.
Now two of my systems use CPU Socket1 & one uses Socket0.
My assessment is that for each BP6, the power delivery & regulation circuity for the CPU sockets is in some stage of failing. Most BP6s will have one socket that is further down the road toward failure. When the newer power hungry CPU is installed, it crosses over the line of being able to run stable. I believe most BP6s have one Socket that's significantly better able to operate its CPU than the other Socket.
This applies for either overclocking older CPUs or installing newer CPUs.
This is why I'm not so eager to launch into the DUAL P-III MOD. I'm holding steady at my new 1.21GHz level for now & maybe the rumored Tualatin adapter will show up soon.