"Does cutting those wires in a different room some how break the connection to the whole thing?" In your case, obviously it did.

It depends on how the jacks are wired. If they are "daisy chained" ... with one wire running from the phone company's input to a series of phone jacks throughout the house, as happens when people decide to add a few jacks and just hook onto the old one, or the original installer decided that chaining was a good way to do it, any jacks that are after the cut will go dead.

Remove the jack you don't want and twist the cut wires together, matching colors. If your internet connection works, that was the problem.

It's a bad idea to have a patched wire in the wall because the patches have a way of going bad. Run new exterior grade phone wire from the phone company's terminator box (where the wires reach the house) to a convenient spot for the DSL box.

Disconnect any wires to jacks you aren't using at the terminator box - they can affect your DSL quality because of ... let's just call it complicated.

Just out of curiosity, do the other phone jacks in the house work?