Why is it trying to connect in the first place? Is there something in Startup that makes it connect? Look at Start/All Programs/Startup. If there is something there, then taking it out of Startup would presumably solve the problem (you could put it on your desktop and click it when you really needed it.)
It is also possible that something else is trying to connect to the internet. I remember it used to drive me crazy when my modem dialup program kept on popping up when I didn't want it to. (Come to think of it, that was a week or two ago -- never did figure out why, so I just uninstalled the software. I can always reinstall if I really need to, e.g. DSL is dead for some reason). For example, I remember way back when I used to have this program to set the PC's clock that was always trying to connect, so I had to change its settings. Just guessing, another possibility might be if your computer is trying to check email at bootup, or if you've got some sort of file sharing program. Maybe stuff like Bonzi Buddy or Kazaa is triggering it -- you have not interactively requested a connection, but some program you've installed is.
If you can't find any obvious suspects, double-check your installation options. Maybe you told it to automatically connect. I remember, back before I got a router, I was using a dedicated PC server, and I had it configured to automatically connect at bootup to the internet. (The program was called Enternet maybe?) But, it could have been configured otherwise. You might try uninstalling and reinstalling the DSL software to see if there is an option somewhere to auto-connect at bootup.
If all else fails, uninstall your dsl software, get a cheap router, and let it make the dsl connection for you.