After checking a few posts on the Fedora forums in the laptops section, I can't find anyone having problems with their rtl8139 ethernet connections. The driver should be in the kernel. Maybe some more info about your hardware, and what version of Fedora your running might help diagnose your problem.
BTW - Back a few years ago, folks complained about this card being shut down by windows. That is, using a communication app in windows that exits by shutting off the card, would leave it disabled in linux. I've never encountered that problem, but there are posts about it in old linuxquestions threads. (This is related to the plug-in cards). Their solution was to pull the card and plug it back in after booting into Linux. I don't know if this will help, but, it's worth a try.