If you spill anything on your Mac, you should immediately power it off and disconnect the charger. I also recommend disconnecting the battery and cleaning the motherboard with alcohol and a toothbrush.
The thing with liquid damage is that it takes a while for liquid to cause corrosion, but once you start sending current through it, the corrosion happens FAST!
I was just watching a video where a repair technician purposely spills a few drops of Coca Cola on the motherboard to see how fast the circuit gets destroyed.
Live webcam Macbook board vs. Coca Cola - YouTube
Some people say you should go to Apple to have your computer fixed. Most likely you'll be quoted over $600 to get it repaired. Not really what I'd spend on an old laptop like that. For that price you can get a decent used Mac. If the hard drive hasn't been liquid damaged, getting the data is easy. It uses a standard SATA hard drive just like any other PC, so all you need is a SATA adapter like this to plug into your new Mac.