I have had Realtek RTL 8139 networking chips on three computers going back to at least VectorLinux 5.8. I've never had a problem with them in VL, either getting them recognized and set up or using them.
As I recall, there are two possible drivers for the 8139 and you need to use the one that's right for your chip. I've used the 8139too (in fact, it's on two of my computers as we speak). The other one is 8139cp. See which one you're using (lsmod), remove it, and try the other one.