So you have a normal (strong) power supply, and the board works with the Pentium Overdrive but not with PCI network cards, right?
So then now try what I wrote, I am repeating it.
"
Try disabling the L2 cache (or removing the module) AND the slowest RAM settings. Yes, no kidding I mean really the slowest setting (most wait states).
Then try again with the PCI network card. If it works, then put again the cache module in, but keep memory setting at slowest and test again.
"
EDIT: I am writing this, because I had a similar problem with an ASUS PVI-SP3. It worked, but not with PCI cards (had crashes).
The board did not like the onboard cache, disabling L2 cache and slow memory setting helped. I then sold the board 😁