One day my Samsung stopped charging, as to my battery was swelling up. The following day I bought a new battery and it is still giving me the same problem. It does not charge or show any sign that it is working. Does anyone know a solution? I've tried many that I've viewed on youtube, but still doesn't work.
Battery swelling up is an indication of battery in terminal stages . It's good that you decided to replace with a new battery
If the new battery is not charging, possible reasons:
a) It could be a rip off battery
b) battery charging is prevented by a transparent plastic foil on the terminals which is preventing contact. Examine carefully and peel it off . See this for a similar issue with S3 batteries Phone only works with busted battery
C) there is a genuine problem with hardware
First eliminate b) then check for a) by borrowing a battery and if both are ruled out, your problem is C) for which only service center can fix
Your USB port maybe damaged. It's very cheap and easy to replace. I did on mine after the phone had trouble charging, and it worked great afterwards.