Yeah... sorry guys. It's been about a week since you both asked this, so I really hope you both found a way to bypass the download mode and get back to the normal home screen, untouched. If not, I hate to be the one to have to say this, but if you haven't gotten past the download mode, your devices are most likely considered "bricked" at this point with very little to no chance of recovering from it.
The G3 Vigor (more so the AT&T variant of the two between AT&T and Sprint) has basically next to ZERO support backing it. This is the first device I've ever seen offered on a major postpaid carrier network that has literally NO fanbase or following. I've been pro-Android since it was released in 2008 and have owned at least two dozen Android devices in that time, and yet for some reason the G3 Vigor is the ONLY one I've seen out of all of them that just never seemed to spark anyone's attention enough to create a community willing to support it. Everything online is for the regular G3, but there are just a few helpful threads for the Sprint variant for some reason, but literally NOTHING WHATSOEVER for AT&T. I'm using a D725 AT&T Vigor that I ditched my Galaxy S5 for because they pulled any chance of rooting it and being able to clean up the hell of a mess that Lollipop caused, but I seriously regret it now. I even tried contacting LG directly in hopes of them providing me a regular stock ROM file to flash it back to, and no dice. Of course LG says to go to AT&T, and AT&T says they don't have one and to go to LG.
The only advice I can offer is that there is still a decent chance that your devices may still be under warranty, as the Vigor was just announced last August or September. Take it to your carrier and have them replace it, so you at least have a device that functions. Then list it on Craigslist or eBay for sale or trade for ANYTHING (EXCEPT the AT&T Galaxy S5). Good luck. I'm sorry. I feel your pain.