Well with it being an Android device running one of 4.X versions of Android doing a hard reset would be a good thing to do.
Plus using the correct external charger for the battery is very important and using a Garmin USB cable too.
3rd party cables is one thing I stay away from when it comes to all my Garmin GPS units.
Example:
And Garmin Monterra came out in 2013 and replacing the battery would be a very good thing to do to start with.
I am not one who would take a Garmin unit apart to try and re-solderer connections.
You would need cold solder so you do not fry the unit.
Cleaning contact areas yes and seeing that they fit tight against the battery.
My son in-law let his eTrex 20 sit of over on year with alkaline batteries in it.
They leak and it could not turn on.
I took a look at the contact area cleaned it with alcohol and let it dry.
Put new batteries in it turned on and also connected to my laptop.
The eTrex does not have a way to charge the batteries they have to be charged with an external charger.
But the bottom line here is:
1. Hard Reset
2. New Battery
3. Correct Garmin USB cable
4. Correct External Garmin Charger
5. Clean the contact areas
6. Make sure the contacts fit good to the battery
Remember this is a very old Garmin unit from 2013 running Android.
If all else fails you can always use an SD card to copy over apps that are needed to be installed or maps.
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