Iphone wont turn on unless plugged in

I went to get a ZAGG invisibleSHIELD done on my iphone, after the installation, my iphone keeps rebooting to the apple logo without going into the menu screen, and the power button (top button) doesn't work.

However, everything works perfectly when it is plugged into a power source (both the wall plug and to a computer). It turns on fine, with as if nothing is wrong. I don't even need the itune to boot it.

Now if unplugged it works fine until the screen turns off automatically. If I were to turn on the phone within seconds then its fine, but if left "off" then the phone refuses to turn back on, until it is plugged into a power source again.
(sometimes it goes back to the apple logo, and does the whole boot up/turn off thing.)

I assumed that some liquid seeped into the phone since nothing was installed, or "changed", but what i don't understand was why the phone works perfectly if plugged in.

I left the phone to "dry" for 24hrs, and now the top power button works, and it was working perfectly fine all afternoon, till an hr ago where it refuses to turn back on again.

So is it some "bug" in the system or is it really that some moisture seeped into the phone?