Excellent - progress at last. Well done.
Well, if no conflicts are being flagged, I'm a bit confused. Unless you've got some legacy hardware in your system which does not have drivers loaded for it (probably unused ISA cards), I'd have thought that conflicts would have been flagged if the resources used by your card were also being used by something else. It is quite normal for PCI devices to share interrupts by the way.
You've tied it down to one PC. Yes?
You bought two new network cards. Is one of these currently in use on your now known good system? If the cards are identical, try swapping then over and see if the good system still works.
I guess you've already done this, but download the latest drivers off the internet for the LAN Card.
You could try removing all of the networking components, rebooting, and set up networking from scratch.
I think you've already tried this too, but try a different PCI slot in your computer.
I hope these suggestions are some use.
Keep us informed!