Along with cleaning the connectors, try this.
With the watch not connected, hold three buttons down (light, down and start buttons) for 15-20 seconds and try charging again.
I just finished chatting with Erica from Garmin Support Centre. The chat took less than 10 minutes and resulted in them sending me a refurbished watch, and I'll send in the defective one when I receive…
Mine wouldn't charge at ALL. I did your trick thinking it wouldn't work as there was no power left but it worked. Thank you!
Thought mine wasn’t charging either. Did this trick and when it powered on, it actually had been charging in the back ground and was at 18%. So it wasn’t that it wasn’t charging it just didn’t power back on after plugging the charging cable in. Thank you, all working now.