The drops on the keyboard could have entered a critical component.

Since more water went underneath, it's possible that some got sucked into the vent and into the fan area and possibly spread elsewhere.

At this point I think I would open up the case to examine various components. Remove the battery and CMOS battery.

Whenever touching components or working inside a computer, wear a grounded wrist strap, also called anti-static wrist strap, ESD wrist strap, or ground bracelet. I know many people do such work without this, but it's a cheap and sensible precaution.

If you see no obvious damage, leave things to dry out for several more days, just to be certain. Afterward,

1. Press and hold the power button for 30 seconds to discharge residual power.
2. Replace the CMOS battery with a new one, in case it shorted. They are inexpensive.
3. Connect the AC adapter
4. Try to boot
5. If no response, unplug the AC adapter, reconnect the battery and try to boot.
6. If no response, try with both battery and AC adapter connected.

P.S. Rice is not helpful. 

Coming back to the same question almost 2 years later, I have the same problem but this time, no water damage no nothing.

By the way, after a long time without the power supply connected as I moved from Cali to Texas, with thjis machine in the storage, it decided to cooperate on its own and powered up. 

Since I did not need another piece of metal with Redmond's finest OS, I installed Ubuntu on it to use it as a home server. Everything ran fine, up until today. In the morning, I got a message that there are softwaare updates pending and I chose to install them. While the software installation/updates were going on, I was doing some light web surfing, when the keyboard and mouse became unresponsive. So, like any other person does, I long pressed the power button to shut it down with the intention of powering it back up few  seconds later.

Now I am into 2-3 hours from the power down and the machine doesn't power up. I opened the back cover, disconnected the battery and let it  sit like 20 minutes. Then, while the battery was disconnected, as advised somewhere, I pressed and hold the power button for 30 seconds or may be a little longer. I attached the battery connector back closed the cover. Now I am back to square one like I was 2-3 hours ago.

Symptoms:

If the power supply is connected, the caps lock light is on even the laptop power is off  As soon as I plug in the power cord, I see the little LED on F4 key blinks. for a fraction of a second and goes off but the caps lock LED stays on.

When I press the power button shortly after, the whole keyboard backlights flash for a fraction of a second and go off again and the caps lock LED turns off. Subsequent presses on the power button generates no visible response.

When I unplug the power supply plug and keep it that way, every time I press the power button, my whole keyboard backlights flash for a fraction of a second and go off but nothing as far as powering up happens.

All this is making me think, some power component, probably a capacitor, holding on to whatever is ailing the laptop from starting up and not letting go, unless a really, really long time, like weeks or months, passes.

How can I fix this issue ? please help.

About an hour later, I disconnected the power supply again and pressed the power button 4 time holding it down about a second each time with a few seconds gap between each press and magically it powered up. Can someone explain me what I did to make it come back alive. I searched dell website about reset sequences but nothing like this comes up.