And just when I was at the verge of deleting this OS, and trying out other Linux distro (which I would suspect be having the same problem), I tried once more to google my way around, indicating the most specific keywords possible. This time, I really did specify everything. So I did "ubuntu 8.10 realtek 8139 ethernet not working", and voila, just on the top of the list are links which doubtedly made sense, yet felt so uninspiring to me. But well, it's something or nothing, so I did check out those sites and finally, yes FINALLY, there's the solution to my problem. I found out it's not Ubuntu that's making this wrong, but it's the chip settings themselves, or probably the setting which Windows initially did after plugging itself on to my system.
Just in case you wanted to know how I did solve the problem with my ethernet connection under Ubuntu, please pay a visit to both of these sites: