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Is the Garmin Approach device new?
If it has never shown anything in the way of signs of life, check whether it even has a battery in it at all. It might have been a prize with batteries not included... it's just a thought.
I see. It may be that the battery included - presumably - is defective.
Try turning it On, while it is connected to the charger (if it is the sort of charger that connects to the device, rather than requiring the removal of the battery. Does it work under those conditions, with the charger attached? if so, then the battery is most likely to need replacing.
Then it may be defective from manufacturer. That means, if you have warranty rights on a prize device - which is possibly unlikely though I haven't read Garmin's warranty terms in detail - you could turn it in to Garmin for a free-under-warranty repair.
See this page:
and the link called 'file a claim' on it.
(If this answers your question, please rate my answer. Thanks.)