If the jack is truly broken internally, then you'll have a hard time finding a replacement unless you try to obtain the original part from LG themselves.
I noticed the device has SMD contacts as shown in the second photo. Is there a couple of through-hole pins underneath the device that cannot be seen in your photos?
Even if you obtained the exact replacement, do you have the tools to make a clean removal and installation of the new part?
I think Bradtherad's suggestions would be your best options until you get a chance to open up the device. If any of the spring contacts are broken, then yes, you'll need to replace it.
Regards,
Relayer