As knute said, we need to know the exact model of the Realtek card; there are a few out there, and they don't all use the 8139too module. A good start would be to open a terminal window and issue the following command (case-sensitive, and the first letter is a lower-case "L"):
lspci -vv |grep Eth
Post the results, and we can take it from there.
If you want, take a look through these troubleshooting steps. They apply only to static addressing, so if you're supposed to be using DHCP, let us know.
DMR
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