iPhone 4 dropped in the toilet briefly and now it won't turn on or be recognized by my computer

Solution 1:

The liquid sensors are only there to determine if the device is still good for warranty, they're placed in strategic spots where the Apple so-called "geniuses" can quickly look and tell you that your device isn't eligible for warranty anymore (even if your problem happens to have obviously nothing to do with water damage).

In fact, the places where the liquid sensors are located on your device (dock and headphone connector) aren't that vulnerable to water and you can usually wipe whatever liquid is in them and the device would still work. This has changed with the iPhone 5 though, and the liquid contact indicator is now inside the SIM tray, which is tightly closed and water is unlikely to get inside accidentally (you'd need to completely submerge the device, in which case it'll completely kill it).

If you happen to be lucky and your device is still under warranty I suggest you go to an Apple Store, you'll get it replaced immediately.