Radio Snack and the home centers will sell you a little adapter that will split the two lines into their own single jack to cut off this apparent interference.

The other option is to carefully remove the jack from the wall and remove the second line from it. This is typically the yellow/black pair if you have red/green/yellow/black wiring or the orange and white pair if you have cat5-style wiring. In any event it will be the outer two of the four pins of the connector (the center two are the first line).

Here is a link that might be useful: two line phone adapter

Thank you SO much - I found an adapter, plugged in my own phone which worked then took out the jack but left the adapter in the wall and the new phone works like a charm - I appreciate your help!