You might try choosing "really small" Windows Display fonts to see if that helps. If that fixes it, then bring the font size up in increments until you get the largest size that doesn't break up. Also, you might try turning off video card acceleration, and, check for a later version of the video card driver.
Did you get a new monitor? If not you could be running the old one at too high a refresh rate with the new computer. Check the monitor driver, too, to make sure you have the right one.