First try unplugging your 2-line phone to see if the feedback is coming through that. If that doesn't work...
I'm not familiar with DSL, but on "regular" lines, you could probably just disconnect the black and yellow wires from the jack that the modem is connected to. (If there are 2 black and 2 yellow on that jack, you should connect the 2 blacks to each other, and the 2 yellows to each other to allow the second line to continue to work on the other jacks in your house.)
More info: usually, there are red, green, black and yellow wires. The red and green are for one line, the black and yellow for the other. If the dsl line is using the red/green pair, then disconnecting the black/yellow pair on that jack might solve the problem, unless the feedback is coming through your 2-line phone.

Just a guess, but use a splitter.

The first reply should work, just disconnect the line that is not your dsl line (from the wall plate) and the modem will work.

Otherwise, I suggest going to phone box (I assume it's readily available for you to access) and install a new line running off the phone line dsl is on. You will see 4 screws - red and green are one line black and yellow are the other. The red and green SHOULD be your primary or first line. Either way figure out which is the dsl line and run that a wire to where you will have your modem. Fish tape will help you run the cord through the wall.

Get a spliiter from Radio Shack. They are only about $7. You plug it into the jack. The other end has 3 openings. One for line 1, one for line 2, and one for a multi-line phone.

Use a splitter or re-wire the phone outlet into seperate jacks for each line.

As I understand it, your phone jack now has all wires for both lines in one plug. Most phone jacks (one line) have only two wires connecting: in the middle of the plug. The second line uses the next two wires from the middle in the plug. A two-line phone keeps them seperate. A one-line phone on this jack only connects to the first line and makes no connection to the other two wires. A DSL modem uses the same wires at different frequencies, and seems to be using both lines, causing them to "short circuit" into each other through the modem.

A splitter routes the middle wires (line 1) and the outer wires (line 2) into different plugs. You can probably use either line for your DSL service. They will not short circuit into each other.