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It's possible that the backlight is the only problem with it - if the times you *can* see anything on the screen, are when direct light is shining right into it. That makes any LCD-type display with a dead backlight, slightly usable.
At very least, the backlight connection has worked loose. At worst, the whole screen needs replacing at minimum - if the sort of screen in your LG Optimus' particular exact model, is the type where the backlight is built into the screen module.
(Let me know your Optimus' exact model #, to hopefully get a more exact estimate as to whether the backlight, if broken, might be separate and replaceable without replacing the screen too.... that would reduce prospective repair cost.)
I advise you to use what little screen readability is left, before something gets worse, to get all your personal data that is stored on the phone - pictures, video, contacts or Address Book, notes or documents - copied off it onto a different device e.g. a computer (or at least a memory card if possible.)
The battery would have the battery model #.
Information on model # ***** can be found, in an Android OS phone, on
Settings - About Device
Settings - About Phone
But if you can find no other info, the battery maker and model # ***** at least narrow down the field considerably, I think.
Your cited battery type would go in an LG Optimus LTE 3 model phone, or also in an LG Optimus F7 phone, etc.
LG's repair-service has two online facilities you might make use of. One is the local service locator:
and the other is this page:
and as for charges you would have to ask. (Also, if the phone is fairly new, and if it is still under the 1-year default warranty from LG, it might be repaired for free under warranty terms.) The turnaround time would be an issue to inquire about with e.g. one of your local LG service providers as located by the facility on the first page cited above.