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How do I set up ps2 network so I could play burnout 3 takedown online?
Of course I have an internet connection so that should do it right?

http://forums.pcsx2.net/Thread-How-To-Play-Online-Guide

of course, that doesn't guarantee it'll work since Dev9 plugin is still buggy and in alpha stage.
moreover, Burnout 3 online servers are probably dead.

Yes, sadly Burnout 3 online servers were shut down several years ago.