I have the exact same problem as OP. Mine's a mid-2012 MacBook Pro, but I may as well attempt to contribute to the discussion...
After drying the laptop, I changed the DC-in board for a working (used) one and cleaned the logic board with 99% isopropyl alcohol, since I thought the DC-in board is most likely to be the source of the problems (the water appeared to mostly touch the MagSafe socket area).
This hasn't helped, which makes me suspect a minor component on the logic board got fried. I can't tell whether or not my attempts at SMC reset have actually worked, since it's hard to get the machine to boot.
However, it has, on a couple of occasions, booted as a result of jigging different MagSafe configurations. By this I mean...
- When I connect the AC cable, the MagSafe LED switches between green and orange.
- I get the same constant faint click/beep as described by OP (coming from the HDD...?).
- Whenever connected to power, the machine seems to be attempting to turn itself on (even if I don't touch the power button), but fails every time.
- Different sequences of plugging-in/unplugging/holding power button/attempting SMC reset, etc. sometimes produces a steady green light on the MagSafe adapter, after which point I can get the laptop to boot for about 10 minutes (just long enough to recover my files!).
On the few occasions it has successfully booted, the fan has been constantly on. So next time I get it into a state where it looks like it might turn on, I'll try another SMC reset instead.
Additionally, when I've got the damned thing to turn on, there's an X in the battery icon. Which is just one more reason to persist with the SMC reset attempts. Yet I'm certain there's also an underlying hardware fault.
Investigations continue.