the kernel built-in driver was not the problem, the driver (called 8139too in vector, rtl8139 in some distros) works well with this card. The problem was the mainboard, maybe BIOS bug. I tried this, put the network adapter in another mainboard, and then run puppy linux live cd and vector linux live cd, both had internet connection, I tried with static ip and dhcp, and in both cases I could open seamonkey and do some googling. This other mainboard I was able to find is similar to the first one, this way I can use my processor, memories and hard disks and all my onboard hardware was recognized be vector.
At first this looked as a problem in my network configuration, then as a problem with my network adapter driver, and at least I found out that the source of problem is the mainboard (BIOS bug?). The mainboard is a PCChips, and old one and there is no more updates in the PCChips home page so I was unable to find a BIOS update (If that is the problem).
Luckily I have a similar mainboard, I'm reinstalling vector right now in the same hard disk but in this new mainboard. My home dir is safe as It is in another partition.
Thank you all for the help, I learned a lot.