It will take a lot longer than 24 hours, especially for a laptop that has little airflow between the tightly-packed components, and especially on the integrated circuits that may have liquid lodged between them. For example, I spilled beer on a keyboard once, an it took that several days to dry after I soaked it in deionized water several times and then set it out to dry.
The best way to dry a system is to use a dessicant (not rice): http://reviews.cnet.com/8301-13727_7-57330736-263/using-desiccants-to-soak-up-we t-electronics/
With a dessicant I would recommend letting it dry for a couple of days, but without it may take a good week to dry. Hopefully the short that caused the shutdown didn't damage anything, and hopefully you can get the liquid out of the system. I would not submerge the system as I described doing with my keyboard, as the hard drive will surely be damaged by the water should it penetrate (there are vents on the drive that will allow water entry). Your best bet would be to open it up as much as possible (take off covers, take out batteries and the hard drive, along with your RAM), and then prop it up to dry out as much as possible (keep using your fan).
The slightest electrical short will prevent it from running, so you may have to wait for it to completely dry to hopefully break all shorts between the circuits (the salts and other charged particles in your juice may dry into an electrically-conductable connection that maintains the short, but hopefully this will not be the case).