Rhooks90, you are not alone. Myself and many others are having the same issue. Your description was perfect to how my phone started to fail. 20%, then 40%, then 65%, then dead. To answer the Verizon Reps question, I did a factory reset from the phone first and it did not help. I then went into the recovery to wipe and reset as well, still no change. I then tried to plug the phone into my computer to back it up or run updates, but the power from my PC will not keep the phone on. I do believe the update may have fried the battery somehow because Verizon sent a replacement and I had the same results, continuous boot loop as soon as I powered it on for the first time. They are sending me a replacement with a new battery to try tomorrow. WOW, now I just got a confirmation email that they are sending me an S5, hopefully it's a typo. Calling you now Verizon.
For backup issues, you may have to get a sizable microSD card, plug in the phone to keep it from rebooting, and then transfer your data using My Files or another file manager app.