First, I would connect the modem to the test jack at the NID and see if the problem continues. If it goes away, the problem is in your wiring. If it continues, the problem is further up the line.
Can't figure out how to do that - there is a DSL splitter in the NID. Can I use one of the other test jacks?
Since they haven't responded to the first email (read the OP), I finally broke down and went through their customer disservice line yesterday. After 45 minutes of things like making sure the modem was plugged in and using a different ethernet cable (I wish I were kidding), they agreed to send out a tech. Unfortunately he won't be here until the day after Christmas...