Sounds like a pretty simple case of shoddy equipment on your landlord's end of things. So you're either going to have to live with it, move, or secure a more reliable form of Internet access for yourself.

If there are any DSL providers in your area, often times they can set up what's called a dry loop, which provides a DSL signal (and no phone service) to a specific phone jack. You'll have to pay for the service of course, but having been in a very similar situation as you a couple of years ago, trust me, it's worth it.