I upgraded my father's PC from its ancient Intel graphics over VGA to a nice AMD/ATI 6450 card over HDMI and experienced this blurry text.
Some things you need to do:
Most TV's have a lot of postprocessing over the HDMI ports. This is what makes your movies and TV look great. However, processing the image on a PC is a no-no. You want the image to look as what the PC is intending the image to look as. So you need to make sure that for the HDMI input is set to a "game" mode or some equivalent mode where there is no postprocessing. If you connect over VGA, manufacturers do not process the VGA input so it looks like what it's supposed to look like and there's no "game" mode as it's unnecessary.
Now you also have to adjust your ClearType settings for this new monitor/TV. Run the settings wizard for ClearType.
You have to adjust your various settings in for your graphics card. Brink has a good pic. Now play with the settings because there's no one set of settings for every display device.
Under My Digital Flat Panels, there's a Properties tab. And under that is GPU scaling and ITC processing. For my father's system, I enabled both of them.
Under the scaling options tab, I've enabled "use the scaling values" and I set overscan to 0% so that the screen takes up the whole screen.
Under Pixel Format, I set RGB 4:4:4. Now this is personal preference. Another pixel format might look better for you.
And I guess the last thing is to know what your true resolution of your LCD panel is. If you have a 720P TV, you have to run your desktop at 1280x720 to get the sharpest image. Similarly, if you have a 1080P TV, you set your desktop to 1920x1080. For example, if your panel is 1440x900, then running at any other resolution besides this resolution will be blurry.