I had exact problem with the watch not turning on after it fully drained, I had to press the "Light" button and the "Power" button at the same time and I got the Triangle and then it displayed the charge…
I am sorry it did not help. Please reach out to your regional Outdoor Product Support for warranty options.
Charging via wall socket? Quicker. Holding down the light button doesn't bring it back to life? Sounds like might have to call support and get a swap out. :-(
Please use the "Will Not Power On" section of this Support Center article - Garmin Outdoor Watch Freezes, Reboots, or Won't Power On