Did you go into Network Settings and try to set up the PS3's connection? You may have to enter more numbers/ change some in there. Another thing would be the modem- you may have to unplug it and then plug it in again to reset it after switching the ethernet cable. If your ISP requires you to log in with a username and password this could cause problems too.
It makes the process so mch easier to get online using a router to share the connection- no cable switching, the router handles the log in, etc.. I would suggest picking one up to be able to have both the PS3 and your computer online on demand.