I had a similar experience with someone's PC a few years ago. Never got to the bottom of it. I took their PC to my house and it worked fine. In their house, there just wouldn't be a dialtone when the modem went off-hook. In fact, their voice mail prompt eventually kicked-in. So, for some reason, the telco switch isn't giving a dialtone. You can rule out the modem as other working modems fail in your house. Evidently it's something subtle to do with the phone point in the house but what that might be I couldn't determine.
Do you have any other phones in your house? If so, unplug them. If not, try plugging one in and then trying dialing out on the modem. Or, try picking up the handset on the other phone and then try dialing out. Just stabbing in the dark here.