Hey guys. I just wanted to go through the troubleshooting process I went through to get my phone charging again.
If you can help it, don't let your LG Connect discharge completely. If it does, it forces you to go through the following steps.
1) Plug the phone into a wall or USB charger. The wall charger is best, and I've found I had better results if I used an iPad charger that delivers 2A of current. (Whether or not this is really better or not is a subject I leave to electrical engineers, but I consistently get faster and better charge times with the lone exception being a car charger being fastest).
2) If the bottom 4 lights are flashing on and off, this is normal, but it seems to require that you wait until the phone has enough charge to power on. If you leave the phone plugged in while it is in this state, it doesn't seem to charge completely, for reasons unknown to me. So as a previous poster said, if you can get it to this step, you're halfway there.
3) Attempt to power on the phone while it is plugged in. If you can get it to the point where the LG symbol appears and a bunch of animations fire off so that it boots, then you are home free. Once the phone is powered up or even if it's not fully booted but shows the battery charge icon, then you are free to plug the phone in.
The phone charges SLOW, whether it's with a 3rd party charger or the included LG Connect adapter. I've been forced to invest in plugs/adapters for mobile use and one at my work, office, and car.
Final suggestion: Investigate power saving apps. The app that I use is called JuiceDefender. It's free, and so far on it's aggressive setting, it's doubled my general use of the phone. Basically, my phone would completely discharge over the course of the day due to the background apps killing it. Juice Defender has customizable settings that basically turns off things like wi-fi and background apps when they are not in use.
There are some challenges with it; at certain power settings if you really want to use the wi-fi, you need to go into the settings and re-enable it, but that may be a result of being on the "aggressive" setting - so your mileage may vary.
The big key is not to panic. Ah, and one other thing.
If you can't even get the flashing lights, then take your phone's back off, and take the battery out for a couple of minutes. This "reset" seems to wake the phone up. If someone can comment as to the "why" that would be great.
I just went through this process (including the panic phase) and now my phone is charging. Hope this helps someone.