I'm with Sami on this one,
When a router is setup in most cases, you probably entered your connection information into it. It can connect all on it's own... which means it would not notify you, except for the local area connection icon. It sounds like a program or programs asking for internet privileges, and attempting through dialup instead of the router. Programs which I have found do this are:
-Wiindows Media Player
-Winamp
-Msn
-some drive imaging tools such as alcohol120% or dameon tools
*A firewall would definatley pin point the offending program(s) then you can deal with it directly
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