You really should mention the exact make and model of the set so a) we have a better idea what the problem is and we can rip into it, how rubbish it is for our own amusement
The xbox 360 is really good in that it has a built in hardware upscaler/downscaler but you must make sure the output resolution and the native resolution of your tv are the same. So if its genuinely a 1080p panel that should be the output setting. Also if your tv has the option, set over-scan to off so you get a 1:1 pixel map. This will effectively turnoff the upscaler of the tv so you don't have 2 upscaler/downscaler effects on the same image.
Some people prefer VGA output from their 360 to TV because it can work better with regards 1:1 pixel mapping and removing overscan on some televisions. Also some televisions have lower input latency over VGA. Seems strange I know as VGA is analogue not digital but might be worth trying if you can borrow a 360 VGA cable.
Televisions nowadays are fantastically well featured and priced. Amazing how much you can get for your money. However at the bottom end (especially in Europe and the far east) most are based on low cost mstar chipsets. These chipsets only cost a few dollars and are reliant to do everything required of processing a input signal and then creating an output image for the panel.
As you can see here boards are incredibly cheap and manufacturers buying in bulk will get better prices than those stated.
http://cndlcd.en.ali...2USB_2HDMI.html
When you say blurry graphics if you mean in motion this is a common picture processing issue related to LCD based panels (includes LED backlit) as they can't update the screen fast enough so the TV's chipset will blur the movement rather than show more juddery movement. This is mainly eliminated by all plasma panels and high end LCD panels which have a much better pixel response rate. If this is the blurring you have check your manual for ways of turning off or lowering picture processing. There may be a game mode you can use.
Edited by Desert Punk, 30 June 2013 - 03:36 AM.