A few random thoughts:
Are you sure you have used microfilters for every device that is plugged into a phone socket, throughout the house? If not then you should do so. If you have, then try unplugging everything from every socket except the modem (and its filter, of course). If you then still have the problem, try a different filter on the modem connection.
You mention "powering up" - does this mean the computer or the modem? If you haven't yet tried switching off the modem, so so. Switch it of, leave it for a few minutes, then switch on again. Then again leave it for a few minutes before you try connecting.
Have you tried using a different cable to connect the modem to the computer, and then to connect the modem to the phone socket? This would ensure that neither cable is faulty.