Not completely. Unless it's an ISP-owned modem/router and cable, try the modem with two different cables connecting it to the test socket and check the same problem occurs with both. There will still be a very small chance that it's the modem socket but I've never heard of that being the case unless the modem's been really yanked out of the wall soon before the problem started.
You forgot this bit at the beginning of my post - "If you are sure that it is not your equipment".