I believe the solution is to configure your working Ethernet as eth0.
Turning the failed on-board NIC OFF in the BIOS is a good start, but, as you've discovered, isn't necessarily the whole solution.
Once you boot into Linux, you should be able to DELETE your current eth0, then RECONFIGURE the working Ethernet as eth0 from the GUI (e.g. from Network Manager).
Failing that, you should be able to edit the appropriate files under /etc/sysconfig/network.
If you're booting only from Live CD (and haven't installed anything to hard disk), all bets are off as to what can or will persist between reboots
'Hope that helps .. PSM