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!
You will need to Bluetooth pair to your smartphone again through the Connect Mobile APP, update your watch settings, and pair any sensors used with your watch.
Everything you prior synced to your Garmin Connect account will remain safe in the cloud. As long as you continue to use the same Garmin Connect account email address when you Bluetooth pair your watch again, you will continue to accrue your daily wellness and saved activities within the same Connect account.
What works best? (If your watch will not charge or power on.)
The reason the method given by "mhyten01" above works so well, is the soft reset being done vs. the actual reset to defaults. A soft reset is holding your top left button until your watch shuts off. Even when your watch is off and will not power on or charge, a soft reset will often fix the issue. If the soft reset process below does not work, you should still try the full reset to defaults too.
If no luck, then try the following:
If your watch did not power on, using the data/charging cable, plug your watch in and charge it using either a wall USB adapter or a PC that is powered on.
If the display lights up and you see your watch charging, odds are now in your favor. Your watch should charge and power on again.
If your display did not light up and there remains no response to being charged: