jiminyt,
If AcaCandy's suggestion is not the answer, you still do have a "program" trying to access the internet, thus attempting to dial up. Usualy suspects include games or demos of games or utilities of some sort. Demos are especially notorious for doing this. Next time that the dial up box pops up there, do the ole ctrl-alt-del key combo and "see" what is running. You may get lucky and see what it is that is trying to access. You may very well end up removing a program, or searching in its settings to disable such a feature.
P.S. I have the option AcaCandy pointed to chkd, but I never get that dial up box unless I have outlook either open, or running in the background, i.e. on start up or having opened it then minimized it to the task bar below.
Good Luck