I have an old Broadcom NetXtreme Gigabit Ethernet NIC, and it worked well with Windows 8.1 but not with Windows 10 (at least not with the version I had).

Anyway, today I managed to find a set of drivers which work. The driver I found is from Lenovo for its THINKSTATION S10 (TYPE 6423, 6483), ver. 10.86.0.0.  Its URL is:
http://support.lenovo.com/us/en/downloads/ds000638

If you are having one of these Braodcom NIC below, you may want to give it try.

5700, 5701, 5702, 5703, 5704, 5705, 5751, 5753, 5754, 5755, 5756, 5782, 5786, 5787, 5788, 5789, 5901, 5906


By the way, the hardware ID for my card is:

PCI\VEN_14E4&DEV_16A6