Welcome to Justanswer.com, my name is Dustin.I'm sorry to hear about the issue you are having, I will do my best to help you resolve it.
Most likely you need to replace the battery, but we may just need to reset the device , t his video will show you how.
After you have reset the device, test and see if it can turn on without the charger.. If not, then you will need to replace the battery.
Here is a replacement guide for the fenix 2, its a great guide and the replacement procedure is almost identical for the fenix 1.
And you can get the battery here
I strive to provide great service, and greatly appreciate a 5 star rating clicked and submitted when you are satisfied.. I always answer follow up questions.Dustin S.Senior Technician and Network Switching Systems Operator / Maintainer.