Phone works when we call out, but doesn't work for incoming calls. When someone calls our phone the person hears one ring then static and then the phone hangs up. We do not hear that one ring from our phone.
First, make sure you phone isn't accidentally forwarded somewhere else by dialing *73 from your home phone.
If that doesn't work, do you have voicemail? Basically, what "should" happen when someone calls you and your on the phone? Does "that" happen if you pick up the home phone and then call it from your cell phone?
It could be something in the house like a fax machine or security system which is picking up the line and then dropping it because of a mechanical problem. Try connecting your house phone directly into the back of the phone modem (instead of wall phone jack) and see if the problem continues.