Just noticed this annoyance this morning. After hitting the Home button in any browser to go to google.com I had to click in the search field to activate it and have a blinking cursor back.....
At first I thought it was related to flash : http://www.mydigitallife.info/mouse-pointer-flickers-blinks-or-disappears-in-web-browser-ie-firefox-google-chrome/, but this was not the case.
It seems recently the basic Google search page has been changed. A workaround to the cursor problem was very simple :
Select Options in the upper right corner and then Search settings :
Scroll down to Google Instant and change setting to Do not use Google Instant :
Another workaround can be : bookmark http://www.google.com/webhp?complete=0 for searching, or set it as your browser home page.