Your computer may be a SpamBot. When you say you disable your connection, how are you disabling it? A sure-fire way is to disconnect the tv cable from the modem or unplug it when not in use.
Comcast can see where the data is going, don't let them lie to you. If they ever complain again make them supply a connection log, they will if the cops ever ask for it, so you can get it too.