Is there a problem with my 1080p Aquos?

Whenever I connect a PS3 to my Sharp Aquos LC42XD1EA TV and select 1080p mode, the picture slowly deteriorates into a green 'snow-like' picture, with frequent sound pops. I've tried the TV with multiple PS3s, and the problem only occurs when selecting 1080p, not 1080i or 720p. I bought this TV because it was advertised with a native 1920*1080p resolution. Is this a fault with my TV? Is it fixable?