The white screen means the back light is working but the screen is not able to "paint" the image on the screen. It is at least the lcd, but you could have damage to additional components.
The cost is relatively minimal to repair.
If you feel comfortable following this guide, go for it; otherwise you could send it to LG. Never had to use the screen repair places in the mall. YMMV.
GUIDE:
https://www.ifixit.com/Guide/LG+G2+L...lacement/28952
Closely inspect everything while you have it open. That way you don't have to repeat the process.
http://www.amazon.com/ePartSolution-...cUvbUpU4126031
This includes the tools required:
http://phonedoctors.com/product/lg-g...d-lcd-display/