As I mentioned, that combination was never going to work with what you have but with a better vrm-capable sloket you do have options.
This is an official cpu compatibility chart (for proper slot 1 cpus only) that Gigabyte issued for their BX board series...
The attachment p3_celeronslot1_cpusupportlist.pdf is no longer available
...so the 6BXE needs a minimum v2.x board + F1 bios to support lower coppermine core voltages. However, a vrm-capable sloket opens up the possibilities of using skt 370 coppermine cpus on even early revision boards. As a good example, my v2.5A GA-6BA doesn't support any slot 1 coppermines but is quite happy to run a skt 370 coppermine 800MHz on the vrm-capable ABit Slotket !!!
In your case, this 2002 quote seems like good place to start assessing what your board version is capable of
"With the the BXE rev 1.9 board the following maximum processor speeds apply.
SLOT 1 - 550MHz Intel Pentium III (Katmai cored processors only) <- These are the
2 volt processors
SLOT 1 - 500MHz - 1000MHz Coppermine cored processors are UNSUPPORTED. <- These
are the 1.65 - 1.75 volt processors.
SOCKET 370 - PPGA - All Intel Celerons to 533MHz
SOCKET 370 - FCPGA - PIII - With the appropriate Slotket (One that is fitted with
an onboard voltage regulator), 850MHz is the official limit for PIII's (That is,
any PIII processor up to 850MHz that uses a 100MHz Front Side Bus).
SOCKET 370 - FCPGA - CELERON - With the appropriate Slotket (One fitted with a
voltage regulator), 1000MHz is the official limit for Celeron's.
SOCKET 370 - FCPGA2 - PIII & CELERON- None! (The Tualatin cored processors are NOT
compatible with this board, even with a PowerLeap convertor as there is NO BIOS
SUPPORT for these processors and as a result, it will not boot)
Slotkets known to work with the BXE that provide voltage regulation are the IWill
Slotket II and the ABit Slotket !!!.
HTH
--
Jeff Cochrane
Jeff's Computers.
Cairns, QLD, Australia."