I'm using a Insignia HDTV with a native resolution of 720p but it can support up to 1080p. I have it connected with a HDMI to my computer. When ever I have text on screen it looks blurry and is hard to look at. I have had it connected to an old lap top I have and it work fine. I have tried different refresh rates, the settings on my TV and my computer but none of it has worked.
You sure it can support 1080p, not 1080i. I would think if it could support it, that its native resolution would be 1080p. If it does happen to be 1080i instead, blurry text is a consequence of interlace video.
Yo Sol, unfortunately, there is (currently) a visible noticeable difference in clarity of text (or graphics to a lesser extent e.g. videos) when using any TV compared to a dedicated PC monitor. Might seem strange, but this has been true for a long, long time.
The best you can do, as has been said by others, is to make sure your TV (native) and PC output resolution matches as close as possible.