It is always worth trying a single NIC installation if it fails with 2 NIC's. If it succeeds you can then enable the second NIC and so an "lspci -v | grep Eth" to identify the card and driver needed.
@Leon, the RTL8111/8168B card may install using the r8169 driver and work a bit, but you need to download and install the r8168 one for it to work properly. Please post back with the result of "uname -r". Tim has ClearOS 6.2 drivers here
. The88E8053 looks like it needs the sk98lin driver. ClearOS 6.2 does not come with it and Tim has not yet compiled any modules for it so you may have to compile your own. If you want to try to disabling one NIC, I'd start with disabling the 88E8053