Jan 1, 2013
I'll run through this from the beginning, basically one day I had it plugged in to my laptop to charge from about 2%, and it started charging and not-charging randomly - I had it locked and every second or two it'd flash between the charging screen and the lock screen + "Connect Your Charger" popup.

After a few seconds of this it up and ran out of battery and switched off, and since then it's failed to pick up any charge at all - I've tried a heap of different USB cables and wall-plug chargers (Samsung, Blackberry, HTC, misc brands) and all I can get is a "frozen" green battery icon for a second or two then a black screen again.
I once got a black screen with red text saying "Battery Low, Unable To Download", and nothing came of that when I left it connected.

I'e tried basically everything I found online - cleaning the port, blowing on the terminals, leaving the battery out for 10 minutes, and nothing worked. I'm borrowing a mate's battery to try it out this weekend but is this more likely to be a problem with the charging port, the battery or something else with the phone? And are there any ways I can fix it? I'm really hoping the solution is right in front of my face.

(To clarify it's not Rooted and it's never been near water.)
that is a good start i think then even before try his charger via wall plug before let us know what happens.
I've seen many many posts regarding issues with the USB port not working (or saying it's charging when it's not plugged in.) Your best bet would be get it replaced at a Samsung Service Centre.
Maybe a bit of an silly suggestion. You haven't got Caffeine installed have you?

I was charging mine and the power requirement of the screen was exceeding the amount of output from the USB charger