Humm tricky, but yes. Actually what they did was good, and you should do it as well, which is covering the contacts with hot glue. Prevents oxiadtion and exposure to air.
Now, what colors wires are connected to the contact below? What I mean is, on the old jack, when you open it, there are 3 contacts (surfaces that are soldered to the wires), one on the right, one on the left and a bigger one below those. To that bigger one there are probably 2 wires connected, and I imagine that they are both equal (i.e. both clear or both white). That's the ground.
When you find out, try connecting those color wires to the same surface on the new jack (don't worry about soldering in yet). Make sure your jack is connected into some source of audio, like an iPod, and that music is playing. Then take the other 2 wires and make one of them touch one of the plugs, for example, the longer one. That' the plug for the sound on your right, so if you hear music coming from your left, you know
you're connecting the left signal wire to the right connector. So when you know which wire is which, use something to mark them, like a small piece of heatshrink on the right. Then you can solder everything in. The diagram below helps (left connector is smaller than right).
