Is your GFI part of an electrical panel and looks like any regular circuit breaker but with a "test" button or is it a type that looks more like a socket (except it has a test button) and installed on a wall?

You said you tried different socket in the house and it all did the same thing. Were all other circuit breakers GFI type also or did non-GFI type tripped as well?

Is your plug 3 prong type or 2 prong type? (in other words, is there a round ground pin?)