the problem I believe is that a textarea uses \n to denote a line break whereas innerHTML uses a <br>
IE seems to be the only one that is really fussy about this, but you can fix it by including a regex to replace those \n's in the function on your "start" page:
Code:
function translateIt(text) {
var text=text.replace(/\n/g,"<br>")
parent.frames['theframe'].googleTranslateElementInit(text);
}