Dump the Celeron - way too fast and too new of a techology to work with the BMDC.
The BMDC will NOT run on a PC motherboard that is faster or newer than a Pentium 133mhz. Just about anything SLOWER should run just fine.
Forget adapter cards or other ginger bread. Find a simple motheboard with ISA sockets and this should get you back up and running.
WHile you're at it, get several as computers of this vintage are NOT easy to find. Fortunately, they're dirt cheap but a PITA to locate.
You may also have a chipset issue. SOme DOS software and programs (BMDC is DOS based), are sensitive to the chipset used by the OEM to link the processor to the rest of the world. Keep in mind that the BMDC was created BEFORE the PCI standard evolved. It would not surprise me if a PCI interface MIGHT not be friendly with the BMDC software.
Revert back to a Pentium 133 or lower motherboard, with ISA slots, and you should be back in touch with real time operation.