The LEC should be able to ping the modem from their office and tell if packets are dropping or not - that should be over the phone and not cost you a dime. If they see the problem on their end, they fix it. If its on your end, you dig deefer.
Last time it happenned to me, I took a laptop and the modem, moved everything to the test jack outside the house, and fired it up. When it worked there, I knew the problem was in my house. Ran a few new cables and it cleared up.