Sounds like something is definitely wrong!
So if I understand it properly,
1) No charge from the wall
2) Charge via USB only
3) No data transfer from USB.
Are you using the same cable when trying to charge from the wall and from the PC? Have you tried using a different outlet, or a different wall charger? Have you tried a different cable?
Also, USB debugging enables you to just "drag and drop" files to and from your phone - without needing to use Kies (Samsung's PC software). I don't use Kies, I have USB debugging enabled and have had no issues. This may be why you can't transfer data.
Going back to your charging issue - first try a different cable. Some cheap cables from eBay or Amazon are built for charging only and do not have the wires for data transfer connected. Also, between a USB port, the cable, the charger, and your phone, the cable is the one thing that is most likely to get damaged. Also try a different outlet and a different wall charger if possible. Right now there are a few variables so its very difficult to tell where your problem lies, so you'll have to try different combinations of wall charger, cable, and outlet to see where the problem lies.
Once you get that narrowed down, let us know - and from there we'll see if we can help more.
Good luck