Internal modem or external modem? Have you tried disconnecting the phone line (and modem power if it has any)? Also, some phone connectors have 4 wires and others have two - I'm not sure how many a computer modem actually needs, so I try to make sure to use the 4-wire connectors just in case - if any wires or connectors were replaced in the "jiggling" process, it's possible that a two-wire piece was inserted (most Y connectors seem to split 4 wires to two pairs of two).

It may not matter - perhaps someone who's bothered to learn what is carried on the various wires will let us know - but it might make a difference.

Good Luck!
JudyB