You said you have a NEO adapter - but, is it the original Neo370, or is it the new Neo370T? Your Cele3-1100/256K chip uses the Neo-370/T
The PIII-1100E/256/100FSB CPU works fine - but only with the Neo370.
Forget the Tualatin core CELE3s & P3s - even with the new Neo, it's no go.
If you want to get the P-III/1100E going:
-place single CPU/Neo370 in socket 370 toward front of PC
- (you did) update your BIOS to RU 1.251 with P3 microcode or later
-set the system FSB to 100MHZ
-set the voltage to 1.75
-get a serious cooler: EverCool 715 or 725 copper w/70mm fan<$20
(powerleap's is barely adequate) +Artic silver + copper shim.
visit nexfan.com for good prices
-get the win2K or winXP driver for HPT366 (better to get Promise card)
(my WinXp BP6 booted, but was not stable running from the HPT366)
Good Luck!