Firstly, with the battery removed, check the resistance between the ring and sleeve terminals of the jack. It should be infinite. If not, there is a short.
If the resistance is infinite, as it should be, then, with no cable inserted, and the battery connected as usual, place the leads between the ring and sleeve terminals of the jack, and measure the current. It should not exceed a couple of milliAmps. If it does, something is wrong.