Can't boot, restarts constantly

Bought a Nexus 5 about 6 months ago USED. It has been amazing. I got the latest OTA a week ago or so, not sure if that has anything to do with current issues.

About 2 days ago started randomly restarting. Today, it shut down and has been in continuous loop restarting. I see "Google" and maybe even the boot dots loading, then it is off. Three seconds later, starts again and repeats. Never makes it all the way into Android system. I let it sit for a while and when I pick it up, without touching any buttons, it repeats all of this. I suppose it is probably dead in general, but I don't know. Do you guys have any ideas? Again, I bought it used and from a ma/pap store who said they buy 100 in bulk, which made me skeptical, but they also had a 60 day guarantee and it was amazing the first 60 days and even after. It has been error free for 6 months, so I don't know if this is just a random issue or if the previous owner dropped it in a lake and I got lucky, or what. FWIW the damn thing has been in a case and never dropped, so it isn't anything that I have done I don't think. Thanks for any help.

edit: never rooted, never messed with, always been stock

V985 constantly rebooting

Hi. So, last night, my phone was sitting and charging when I started hearing it vibrate. I looked at it and saw that it was suddenly on the Verizon splash screen. No big deal, it just reboot for whatever reason. But then it kept doing it. It boots up, gets to the lockscreen, starts loading things, and then kicks back out to the Verizon screen.

Reflashing everything fixes it. Safe mode does not. It doesn't happen in recovery mode either.

I've pretty much resigned myself to having lost this, though I did make a backup of everything, restoring it just causes the problems to come up again.

Is there any way I can keep it stable long enough to at least back up the contacts and stuff? Or a way to kill whatever is causing it?