Thanks for your question.
Sorry for your troubles.
From what you are describing, it soukds like your battery may be the reason for your problems.
Because you are getting the charging icon when you connect the charger, the usb cord, charging block and charge port seem to be working.
What isn't happening is the battery is not taking the charge that the cable and block and charge port are giving it.
The first and cheapest way to test a solution is to replace your battery. Make sure the new battery is an OEM (Original Equipment Manufacturer) one. If someone suggests something else other than a Samsung battery, tell them to shove off.
I just checked prices and a new battery shouldnt be more that 20 to 30 bucks.
If the issue pursists then seek out a trusted cellphone repair professional for power issues. Those, for the most part, are straightforward repairs.
Hope this helps.