The apartment was built in 1974, and the phone wiring is showing its age. The main outlet is a mess, but it works. My ISP tech support told me that there was a problem in my phone wiring. My cheap Radio Shack wiring tester told me that it had reversed polarity, which I know is wrong and can cause problems with some phone systems. As soon as the rain stops, I will search out where the phone wires come into my apartment. Then I can start to understand how the system is wired. I have a digital multimeter. There is no attic to run the wires through, so the phone wires must go through the walls. Wish me God's Blessing in finding the problem, since the manager offers no help.

No need to wait for the rain to stop. Just go down in the basement and look for it and switch the red and green.

If one jack works, then the problem is not likely in the main terminal. Phone wiring is most often daisy chained. Which means the wiring goes from the terminal to one jack then on to the next jack and so on.

Unless you want to trace the wiring through the walls, I would just run wires from working jack along the baseboard.

Some more details about the apartment might help. Is it part of an apartment building? A multi-family home or what?

Like ScottGem mentions, Most phone wiring is Daisey chained. I Install Phone systems as well so I like to home run them all. More capabilities. I would remove both jacks and check the colors of the wires, as well as the outside box.
With your meter, you should see 50 Volts DC on the line, the Red is Negative and the Green is positive. As mentioned, reversing at the jack will correct the reverse polarity.
Good Luck