Hi, Jayalin, I'm about to become someone's Fresh Meat Entree soon too. I believe that PBW works by transferring turn files before you start and after you're done. You don't need to stay on for any length of time - you just need to D/l and U/l your turn file. I think the files are something in the 100's of K, not too bad for dial-up unless you're still running at 14400.
I tend to be a push over for the Unmodded AI as well, though lately, i seem to be getting better thanks to some tips on this site as well as #se4 on gamesnet IRC. Building a couple of space stations with spaceyards in them, cranking out Colony Ships from all three, and spreading your seed like a sports figure is a good way to up on the game early. It also seems to cause the AI to "respect" you more - they'd rather ally with you than crush you out of hand. Your Mileage May Vary, of course. You do need to be a fairly agressive player - that was my problem; I was willing to grow slowly, and the AI ate planets and excreted ships. Guess who won those games?
Keep at it though; even if you lose, as long as you learn something and/or have fun, it's not a waste of time.