Hallelujah, there was actually a simple answer to this. My friend took the phone and cord in and it turned out there was something wrong with the cord. Wasn't it supposed to be brand new? Anyway, they've been having trouble with some of the inner prongs (?) falling out, which I'd never heard of, but he was doubly lucky because he was missing only 1 of maybe 5 instead of 2 or 3, and he got a free, though I think used, replacement. The phone's working fine now.