Wired connection. The computer and router are literally less than a foot away from the phone jack. BUT I just found out that the connection only cuts out when someone's using the phone. Hmm.
I think they hooked it up wrong or something...
The funny thing is, my mom is a manager at the company who provides our internet service.
Well, it turns out we just forgot to put DSL filters on all the phones. *facepalm*
I was wondering if that might be the case as I was reading the first couple of posts... I was going to post that as a possible solution, but I see you discovered that already.