I've seen this issue quite a bit. What you need to do is: 1) remove the back glass and unplug the battery and remove it. 2) Remove the Emi shield that covers the LCD connector 3) inspect the board and you will see a black big chip (the wifi IC). Looking straight down with the charging pins closer to you, it'll be on the right next to the LCD connector. 4) THE FIX - you need a hot air type of tool. I'm not sure if a hair dryer will do the trick, but I use a heat gun. You need to apply slight amount of heat. NOT a lot. Just enough to get it hot but not too hot (too hot = you can't touch) like I said, slight heat. 5) put the phone back together and voila. Works! I've seen roughly 3 phones already same issue same fix. No warranties so far.
Apple will not fix this computer any longer because it is considered "vintage". If you can get the part from www.powerbookmedic.com or www.dvwarehouse.com you could always try installing it yourself. PowerBookMedic also has a "Send IN" Logic Board repair program that would save you some money if you want to get your logic board fixed. Hope this helps.
You could definitely try hooking it up to an external monitor to see if the machine is still functioning properly. Also try a PRAM reset to see if that will do anything. It could be a number of things if liquid was spilled into the unit. Check the MLB to see if there is any corrorsion or liquid damage.