Might be the charger, so try a new one if you like. But don't be surprised if you end up having to replace the USB board after. The issues you described with booting/not booting sound like symptoms of the USB board on the fritz.
When the boards start dying, they rarely stop working completely (at least initially), and often show a couple of faults, but work OK in other ways (might be able to transfer data OK but can't charge as an example, and so on).
As a test, do a completely clean install of stock & test it for a few days, if you see the same thing, it's fairly likely the hardware fault. Up to you which way you want to go in that case, but I'd be replacing the board.
Edit - In light of your post just now which crossed with my reply, it's definitely the USB board. You've tried different chargers, you've tried stock, that seals the deal as far as I'm concerned. Put it this way, if it's not the board, it's something else hardware-wise.
If it's important enough to cause you grief if it's lost, back it up. No excuses
Trolling for thanks is lame
Does Samsung's auto-brightness implementation crap drive you to self-harm ? A solution !
Failure to search is the leading cause of male impotence on XDA
If you don't know how to recover if things go wrong, what are you doing flashing custom roms ?