Ok, so you have DSL. That helps a bit.

DSL runs on your phones lines but it has to go through a modem for your computer to make any sense of it. The modem will look like a box with lights on it, and it will have several ports in the back to plug various lines in.

There will be a line that goes from the phone jack into the modem, then a line that goes from the modem to your computer or to a router.

Since you keep mentioning only one device, I am going to assume you actually have just a modem and NOT a router.

First, make sure your line is unfiltered. When they install DSL service on your phone lines they might have given you some inline filters, little tiny boxes that plug into the wall and then you plug your phone into those. Make sure none of those are between the modem and your wall jack. Those boxes filter out the data signal from the line so your normal phone will work correctly. If the filter is on the modem line, it will lose signal.

If that isnt the case, call your DSL provider and tell them you are having problems with the connection. They use the absolute cheapest hardware available so it's easily possible you got a bad one. They should replace it for free, and troubleshoot your lines as well. If you are out in the sticks and at the end of a run you can have signal issues as well as it degrades with distance.

Now, if you DO have a router, it will probably look a lot like the modem. It's basically a small, specialized computer that handles traffic. It is what lets all the computers and devices on your network get the information they requested without getting confused with the other devices. If you have one, it will be plugged in to your modem, and your computer will plug in to that. IF you did have one, you could remove it from the system and go direct into the modem.

Now, since it seems like you don't actually have a router you are a bit exposed as I mentioned before. If you would like some more advice about how to protect your computer from malicious users, let me know and I can post some helpful tips that even a technophobe can understand.