I've been in your shoes before. I know how frustrating drivers can be for esoteric hardware. Considering the tendency of some network card manufacturers to flip-flop chipsets as well as relabel them (I love you, D-Link), that task can be substantially more difficult than it should be. Of course, the problem is compounded when having to deal with PEBCAK. A user who's invested in finding a solution with a tint of experience is an excellent start to achieving a solution, but such users seem too few when swimming in the sea of indifference.
However, in this case, the OP had identified the NIC as using the RTL8139 chipset. The 8139 has been stable for a long time with few sub-revisions, so I'm not afraid to recommend drivers from the hardware vendor.