Well if it showed a screen that said "fastboot mode" then at least we know that the display is working.
I'm not familiar with LGs, and as they stopped making phones that's unlikely to change, but in general fastboot mode is good, since that's the mode you'll need to reflash the system. You'll need a different driver on your PC, since the device is not running android and so will have different protocols, but a Web search for LG fastboot driver should find you something. Fastboot itself is a command line program you have to install on the computer, which you can then use to flash firmware to the phone.
The catch is the details, since I'm not familiar with LGs. You say you tried to flash it, but what tool did you use to do that? Do you already have the firmware in a zip file, or is it wrapped up in some other package (e.g. HTC used to release windows .exes which contained the firmware they would flash), and if so what is it called? If we are lucky someone who knows LG will see this, but otherwise this information may give us some clues as to where to start.
Also as I know LG released different versions of some phones, do you have the full model number just in case?