GPS will not charge
The GPS will not charge, ie. , accept external power. GPS still show some charge on battery so any guessing it is another problem.
It it works on external power but won’t charge the battery, perhaps the battery is failing and needs to be replaced. Even rechargeable batteries have a lifespan.
Here’s a link to the ifixit Removing the Garmin Nuvi 1300 LCD touch Screen assembly guide.
Whilst this is not the problem in your GPS, the guide is useful as it shows how to open the GPS so that access to the battery is possible.
Replacement batteries are available online, just search for Garmin Nuvi 1300 replacement battery to get results for suppliers.
Here are some links to suppliers. They are only shown to give an idea of the cost of the part etc.
There are other suppliers online that may suit you better.