If your connection is wireless, as opposed to ethernet cable, what is the strength of your password? Is it WEP or WPA? What flavor of WPA (encryption e.g.)? Do you use that password anywhere else? If wireless, other users can use your connection unless you have it securely locked.
Confused a little . . . what do you mean by "Internet related"?
When you say your router is "passworded", are you talking about the typical password to get into the router management console, or are you talking about your ISP password?
Do you cut and paste your passwords from a password manager, or do you use the keyboard and type it in? Using the keyboard exposes you to keylogger malware.
Call your ISP and change your ISP password. (Unless they know about the change, your connection will be refused, so tell them BEFORE you make the change.)
Have you run an on-demand scan of your antivirus program? (Are definitions up to date?)