How should I hook up this phone jack?
These Jacks can be difficult and are often a one time install product. The wire may not simply have 'pulled out' from it, the copper conductor may have actually broken off inside the unit OR the tabs that make contact with the conductors could be broken inside.

Even if you able to push in newly stripped wires and have them 'grab tight' and stay mechanically connected, there may be conductors inside the jack that do create a closed circuit.

You'll spend far less time and energy replacing with new, than troubleshooting and/or repairing these mass produced units.

Good luck. Let us know if you have a solution.