I just yum-installed the 2.6.9-34 kernel RPMs and rebooted, and lo and behold, my other onboard NIC is now detected, after a fashion. /etc/sysconfig/hwconf now has entries for:
device: eth0 driver: forcedeth desc: "nVidia Corporation CK804 Ethernet Controller"
device: eth2 driver: sky2 desc: "Marvell Technology Group Ltd. 88E8053 Gigabit Ethernet Controller"
The device/desc lines for both were always there, but previously the device now identified as eth2 had neither a driver assigned nor a recognized hwaddr, and if I disabled either device in the BIOS, then the remaining enabled device would take on the same driver/hwaddr that has otherwise been listed for eth0.
The odd thing still is that according to the motherboard manual, the two onboard NICs are identical, so I still don't know why one shows up as nVidia and the other as Marvell. If I wasn't afraid of messing up my working configuration I'd try deleting them both and letting them be rediscovered, just to see if anything else changes.