I recently purchased a new 55 inch LED HDTV, I hooked my ps3 up to it (HDMI) and now I experiance about a half a second delay when I press a button and the action is preformed on the TV. This never happened on my old TV, I've looked around and can't find any solutions help! I'm using a Kogan KALED55XXXWA and as far as I know there isn't a game mode.
Input lag is generally controlled by the TV and generally not something you can affect yourself, outside of using "game mode". If possible, things like disabling higher than 60Hz display modes and any form of postprocessing can help display lag, but there's often no option for doing this outside of "game mode". You can try disabling any advanced video features the TV allows you to and see if that decreases lag.
This is why it's important to check the input lag of a TV or monitor before purchasing, as it's for the most part out of your control. Make sure you're not using a capture device device between the PS3 and TV as those can introduce lag as well; I personally use a splitter to get the feed direct to the TV and direct to the capture card. If you're using a splitter, make sure it's a powered splitter.
This review indicates the Kogan LED 55" TV might have upwards of 70ms of input lag, which is fairly bad.