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This sounds very much like a common problem with some older T2x systems. In those, the laptop has what's been termed the "Blink of Death". Only the hard drive LED flashes for a brief time when the power button is pushed. Left alone for some time, usually without power of any kind, they may boot again. As far as I know no definite solution has been found but suspicion points to one or more of the power controller circuits as the root cause.
My guess is that there's still some residue on the motherboard from the spill that's causing this problem. About the only way I know of to fix it would be to remove everything that resides in sockets (memory, CPU, CMOS battery, PCI Express Mini, modem, etc.) or bolts to the board (PC Card, etc.) and submerge the board in distilled
water and lightly scrub it (both sides) with a soft toothbrush. Allow it to air dry for a couple of days. Re-assemble everything and see what happens. The worst thing that could occur would be that the board never powers up again and then you're left with the decision to replace the motherboard or recycle the system; about the same choices you have right now.
A more precision approach would be to inspect/clean the areas around any of the power controller ICs. Those can be found by looking for Maxim (MAX) or Analog Devices (ADP) logos or part numbers. Something along the lines of MAX1901 or ADP3207. Murphy's Law would say that those parts would be on the bottom side of the motherboard but take a close look at the top side before you remove the board. For in-place motherboard cleaning I would use some 90+% isopropyl alcohol dipped cotton swabs. It might be possible to use some commercially available printed circuit board cleaners but you have to be careful that they don't attack any of the plastics. Some of those solvents can turn plastic into a goo