Damn, damn, damn

In amongst the spam (Demon's filter has been distinctly falling behind in its Red Queen's Race of late) we've just received seven non-receipt notifications to e-mails we never (knowingly) sent with addresses that don't exist.
I assume that this means that our computer is an evil zombie spam-monster, heaven knows how it got infected. Does anyone know what we should do next? (thinks: this is why I don't do online banking).