Something is up with those Ethernet cards if removing the unused pairs "fixes" the problem. Both 10BaseT and 100BaseTX use the same pairs of wires in CAT3 and CAT5 cable. the only difference in the cable catagory is the quality rating and shielding. Both have 8 wires (4 pairs). I think the unused pins of the RJ-45 connector on Ethernet devices are left floating and not connected to anything beyond the jack. I wouldn't be surprised if these picky cards do something silly like grounding those pins, which is really bad practice considering those lines could be carrying Power Over Ethernet.

That being said, I have never run into this problem with 10BaseT NICs not interfacing with auto-negotiating hubs. That includes cards based on the SONIC series chip used in 68k Macs, the Fastpath 4, and Nubus cards (its used in just about every 3rd party Macintosh NIC since its register compatible with Apple's built-in NIC drivers). All my patch cables have all 8 wires crimped in the RJ-45 jacks.